8.5 Adding and subtracting rational expressions (Page 2/2)

<< Chapter < Page

Elementary algebra Page 2 / 2

Chapter >> Page >

$\begin{array}{l} \frac{3 x^{2} + 4 x + 5}{(x + 6) (x - 2)} + \frac{2 x^{2} + x + 6}{x^{2} + 4 x - 12} - \frac{x^{2} - 4 x - 6}{x^{2} + 4 x - 12} \\ Factor the denominators to determine if they're the same . \\ \frac{3 x^{2} + 4 x + 5}{(x + 6) (x - 2)} + \frac{2 x^{2} + x + 6}{(x + 6) (x - 2)} - \frac{x^{2} - 4 x - 6}{(x + 6) (x - 2)} \\ The denominators are the same . Combine the numerators being careful to note the negative sign . \\ \frac{3 x^{2} + 4 x + 5 + 2 x^{2} + x + 6 - (x^{2} - 4 x + 6)}{(x + 6) (x - 2)} \\ \frac{3 x^{2} + 4 x + 5 + 2 x^{2} + x + 6 - x^{2} + 4 x + 6}{(x + 6) (x - 2)} \\ \frac{4 x^{2} + 9 x + 17}{(x + 6) (x - 2)} \end{array}$

Got questions? Get instant answers now!

Practice set a

Add or Subtract the following rational expressions.

$\frac{4}{9} + \frac{2}{9}$

$\frac{2}{3}$

Got questions? Get instant answers now!

$\frac{3}{b} + \frac{2}{b}$

$\frac{5}{b}$

Got questions? Get instant answers now!

$\frac{5 x}{2 y^{2}} - \frac{3 x}{2 y^{2}}$

$\frac{x}{y^{2}}$

Got questions? Get instant answers now!

$\frac{x + y}{x - y} + \frac{2 x + 3 y}{x - y}$

$\frac{3 x + 4 y}{x - y}$

Got questions? Get instant answers now!

$\frac{4 x^{2} - x + 4}{3 x + 10} - \frac{x^{2} + 2 x + 5}{3 x + 10}$

$\frac{3 x^{2} - 3 x - 1}{3 x + 10}$

Got questions? Get instant answers now!

$\frac{x (x + 1)}{x (2 x + 3)} + \frac{3 x^{2} - x + 7}{2 x^{2} + 3 x}$

$\frac{4 x^{2} + 7}{x (2 x + 3)}$

Got questions? Get instant answers now!

$\frac{4 x + 3}{x^{2} - x - 6} - \frac{8 x - 4}{(x + 2) (x - 3)}$

$\frac{- 4 x + 7}{(x + 2) (x - 3)}$

Got questions? Get instant answers now!

$\frac{5 a^{2} + a - 4}{2 a (a - 6)} + \frac{2 a^{2} + 3 a + 4}{2 a^{2} - 12 a} + \frac{a^{2} + 2}{2 a^{2} - 12 a}$

$\frac{4 a^{2} + 2 a + 1}{a (a - 6)}$

Got questions? Get instant answers now!

$\frac{8 x^{2} + x - 1}{x^{2} - 6 x + 8} + \frac{2 x^{2} + 3 x}{x^{2} - 6 x + 8} - \frac{5 x^{2} + 3 x - 4}{(x - 4) (x - 2)}$

$\frac{5 x^{2} + x + 3}{(x - 4) (x - 2)}$

Got questions? Get instant answers now!

Fractions with different denominators

Sample set b

Add or Subtract the following rational expressions.

$\begin{array}{l} \frac{4 a}{3 y} + \frac{2 a}{9 y^{2}} . & The denominators are n o t the same . Find the LCD . By inspection, the LCD is 9 y^{2} . \\ \frac{}{9 y^{2}} + \frac{2 a}{9 y^{2}} & \begin{array}{l} The denominator of the first rational expression has been multiplied by 3 y, \\ so the numerator must be multiplied by 3 y . \\ 4 a \cdot 3 y = 12 a y \end{array} \\ \frac{12 a y}{9 y^{2}} + \frac{2 a}{9 y^{2}} & The denominators are now the same . Add the numerators . \\ \frac{12 a y + 2 a}{9 y^{2}} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{3 b}{b + 2} + \frac{5 b}{b - 3} . & \begin{array}{l} The denominators are n o t the same . The LCD is (b + 2) (b - 3) . \end{array} \\ \frac{}{(b + 2) (b - 3)} + \frac{}{(b + 2) (b - 3)} & \begin{array}{l} The denominator of the first rational expression has been multiplied by b - 3, \\ so the numerator must be multiplied by b - 3. 3 b (b - 3) \end{array} \\ \frac{3 b (b - 3)}{(b + 2) (b - 3)} + \frac{}{(b + 2) (b - 3)} & \begin{array}{l} The denominator of the second rational expression has been multiplied by b + 2, \\ so the numerator must be multiplied by b + 2. 5 b (b + 2) \end{array} \\ \frac{3 b (b - 3)}{(b + 2) (b - 3)} + \frac{5 b (b + 2)}{(b + 2) (b - 3)} & \begin{array}{l} The denominators are now the same . Add the numerators . \end{array} \\ \frac{3 b (b - 3) + 5 b (b + 2)}{(b - 3) (b + 2)} & = & \frac{3 b^{2} - 9 b + 5 b^{2} + 10 b}{(b - 3) (b + 2)} \\ = & \frac{8 b^{2} + b}{(b - 3) (b - 2)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{x + 3}{x - 1} + \frac{x - 2}{4 x + 4} . & \begin{array}{l} The denominators are n o t the same . \\ Find the LCD . \end{array} \\ \frac{x + 3}{x - 1} + \frac{x - 2}{4 (x + 1)} & The LCD is (x + 1) (x - 1) \\ \frac{}{4 (x + 1) (x - 1)} + \frac{}{4 (x + 1) (x - 1)} & \begin{array}{l} The denominator of the first rational expression has been multiplied by 4 (x + 1) so \\ the numerator must be multiplied by 4 (x + 1) . 4 (x + 3) (x + 1) \end{array} \\ \frac{4 (x + 3) (x + 1)}{4 (x + 1) (x - 1)} + \frac{}{4 (x + 1) (x - 1)} & \begin{array}{l} The denominator of the second rational expression has been multiplied by x - 1 \\ so the numerator must be multiplied by x - 1. (x - 1) (x - 2) \end{array} \\ \frac{4 (x + 3) (x + 1)}{4 (x + 1) (x - 1)} + \frac{(x - 1) (x - 2)}{4 (x + 1) (x - 1)} & \begin{array}{l} The denominators are now the same. \\ Add the numerators. \end{array} \\ \frac{4 (x + 3) (x + 1) + (x - 1) (x - 2)}{4 (x + 1) (x - 1)} \\ \frac{4 (x^{2} + 4 x + 3) + x^{2} - 3 x + 2}{4 (x + 1) (x - 1)} \\ \frac{4 x^{2} + 16 x + 12 + x^{2} - 3 x + 2}{4 (x + 1) (x - 1)} & = & \frac{5 x^{2} + 13 x + 14}{4 (x + 1) (x - 1)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{x + 5}{x^{2} - 7 x + 12} + \frac{3 x - 1}{x^{2} - 2 x - 3} & Determine the LCD . \\ \frac{x + 5}{(x - 4) (x - 3)} + \frac{3 x - 1}{(x - 3) (x + 1)} & The LCD is (x - 4) (x - 3) (x + 1) . \\ \frac{}{(x - 4) (x - 3) (x + 1)} + \frac{}{(x - 4) (x - 3) (x + 1)} & The first numerator must be multiplied by x + 1 and the second by x - 4. \\ \frac{(x + 5) (x + 1)}{(x - 4) (x - 3) (x + 1)} + \frac{(3 x - 1) (x - 4)}{(x - 4) (x - 3) (x + 1)} & The denominators are now the same . Add the numerators . \\ \frac{(x + 5) (x + 1) + (3 x - 1) (x - 4)}{(x - 4) (x - 3) (x + 1)} \\ \frac{x^{2} + 6 x + 5 + 3 x^{2} - 13 x + 4}{(x - 4) (x - 3) (x + 1)} \\ \frac{4 x^{2} - 7 x + 9}{(x - 4) (x - 3) (x + 1)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{a + 4}{a^{2} + 5 a + 6} - \frac{a - 4}{a^{2} - 5 a - 24} & Determine the LCD. \\ \frac{a + 4}{(a + 3) (a + 2)} - \frac{a - 4}{(a + 3) (a - 8)} & The LCD is (a + 3) (a + 2) (a - 8) . \\ \frac{}{(a + 3) (a + 2) (a - 8)} - \frac{}{(a + 3) (a + 2) (a - 8)} & The first numerator must be multiplied by a - 8 and the second by a + 2. \\ \frac{(a + 4) (a - 8)}{(a + 3) (a + 2) (a - 8)} - \frac{(a - 4) (a + 2)}{(a + 3) (a + 2) (a - 8)} & The denominators are now the same . Subtract the numerators . \\ \frac{(a + 4) (a - 8) - (a - 4) (a + 2)}{(a + 3) (a + 2) (a - 8)} \\ \frac{a^{2} - 4 a - 32 - (a^{2} - 2 a - 8)}{(a + 3) (a + 2) (a - 8)} \\ \frac{a^{2} - 4 a - 32 - a^{2} + 2 a + 8}{(a + 3) (a + 2) (a - 8)} \\ \frac{- 2 a - 24}{(a + 3) (a + 2) (a - 8)} & Factor - 2 from the numerator . \\ \frac{- 2 (a + 12)}{(a + 3) (a + 2) (a - 8)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{3 x}{7 - x} + \frac{5 x}{x - 7} . & \begin{array}{l} The denominators are n e a r l y the same. They differ only in sign. \\ Our technique is to factor - 1 from one of them. \end{array} \\ \frac{3 x}{7 - x} = \frac{3 x}{- (x - 7)} & = & \frac{- 3 x}{x - 7} & Factor - 1 from the first term . \\ \frac{3 x}{7 - x} + \frac{5 x}{x - 7} & = & \frac{- 3 x}{x - 7} + \frac{5 x}{x - 7} \\ = & \frac{- 3 x + 5 x}{x - 7} \\ = & \frac{2 x}{x - 7} \end{array}$

Got questions? Get instant answers now!

Practice set b

Add or Subtract the following rational expressions.

$\frac{3 x}{4 a^{2}} + \frac{5 x}{12 a^{3}}$

$\frac{9 a x + 5 x}{12 a^{3}}$

Got questions? Get instant answers now!

$\frac{5 b}{b + 1} + \frac{3 b}{b - 2}$

$\frac{8 b^{2} - 7 b}{(b + 1) (b - 2)}$

Got questions? Get instant answers now!

$\frac{a - 7}{a + 2} + \frac{a - 2}{a + 3}$

$\frac{2 a^{2} - 4 a - 25}{(a + 2) (a + 3)}$

Got questions? Get instant answers now!

$\frac{4 x + 1}{x + 3} - \frac{x + 5}{x - 3}$

$\frac{3 x^{2} - 19 x - 18}{(x + 3) (x - 3)}$

Got questions? Get instant answers now!

$\frac{2 y - 3}{y} + \frac{3 y + 1}{y + 4}$

$\frac{5 y^{2} + 6 y - 12}{y (y + 4)}$

Got questions? Get instant answers now!

$\frac{a - 7}{a^{2} - 3 a + 2} + \frac{a + 2}{a^{2} - 6 a + 8}$

$\frac{2 a^{2} - 10 a + 26}{(a - 2) (a - 1) (a - 4)}$

Got questions? Get instant answers now!

$\frac{6}{b^{2} + 6 b + 9} - \frac{2}{b^{2} + 4 b + 4}$

$\frac{4 b^{2} + 12 b + 6}{{(b + 3)}^{2} {(b + 2)}^{2}}$

Got questions? Get instant answers now!

$\frac{x}{x + 4} - \frac{x - 2}{3 x - 3}$

$\frac{2 x^{2} - 5 x + 8}{3 (x + 4) (x - 1)}$

Got questions? Get instant answers now!

$\frac{5 x}{4 - x} + \frac{7 x}{x - 4}$

$\frac{2 x}{x - 4}$

Got questions? Get instant answers now!

Sample set c

Combine the following rational expressions.

$\begin{array}{l} 3 + \frac{7}{x - 1} . & Rewrite the expression. \\ \frac{3}{1} + \frac{7}{x - 1} & The LCD is x - 1. \\ \frac{3 (x - 1)}{x - 1} + \frac{7}{x - 1} & = & \frac{3 x - 3}{x - 1} + \frac{7}{x - 1} & = & \frac{3 x - 3 + 7}{x - 1} \\ = & \frac{3 x + 4}{x - 1} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} 3 y + 4 - \frac{y^{2} - y + 3}{y - 6} . & Rewrite the expression. \\ \frac{3 y + 4}{1} - \frac{y^{2} - y + 3}{y - 6} & The LCD is y - 6. \\ \frac{(3 y + 4) (y - 6)}{y - 6} - \frac{y^{2} - y + 3}{y - 6} & = & \frac{(3 y + 4) (y - 6) - (y^{2} - y + 3)}{y - 6} \\ = & \frac{3 y^{2} - 14 y - 24 - y^{2} + y - 3}{y - 6} \\ = & \frac{2 y^{2} - 13 y - 27}{y - 6} \end{array}$

Got questions? Get instant answers now!

Practice set c

Simplify $8 + \frac{3}{x - 6} .$

$\frac{8 x - 45}{x - 6}$

Got questions? Get instant answers now!

Simplify $2 a - 5 - \frac{a^{2} + 2 a - 1}{a + 3} .$

$\frac{a^{2} - a - 14}{a + 3}$

Got questions? Get instant answers now!

Exercises

For the following problems, add or subtract the rational expressions.

$\frac{3}{8} + \frac{1}{8}$

$\frac{1}{2}$

Got questions? Get instant answers now!

$\frac{1}{9} + \frac{4}{9}$

Got questions? Get instant answers now!

$\frac{7}{10} - \frac{2}{5}$

$\frac{3}{10}$

Got questions? Get instant answers now!

$\frac{3}{4} - \frac{5}{12}$

Got questions? Get instant answers now!

$\frac{3}{4 x} + \frac{5}{4 x}$

$\frac{2}{x}$

Got questions? Get instant answers now!

$\frac{2}{7 y} + \frac{3}{7 y}$

Got questions? Get instant answers now!

$\frac{6 y}{5 x} + \frac{8 y}{5 x}$

$\frac{14 y}{5 x}$

Got questions? Get instant answers now!

$\frac{9 a}{7 b} + \frac{3 a}{7 b}$

Got questions? Get instant answers now!

$\frac{15 n}{2 m} - \frac{6 n}{2 m}$

$\frac{9 n}{2 m}$

Got questions? Get instant answers now!

$\frac{8 p}{11 q} - \frac{3 p}{11 q}$

Got questions? Get instant answers now!

$\frac{y + 4}{y - 6} + \frac{y + 8}{y - 6}$

$\frac{2 y + 12}{y - 6}$

Got questions? Get instant answers now!

$\frac{y - 1}{y + 4} + \frac{y + 7}{y + 4}$

Got questions? Get instant answers now!

$\frac{a + 6}{a - 1} + \frac{3 a + 5}{a - 1}$

$\frac{4 a + 11}{a - 1}$

Got questions? Get instant answers now!

$\frac{5 a + 1}{a + 7} + \frac{2 a - 6}{a + 7}$

Got questions? Get instant answers now!

$\frac{x + 1}{5 x} + \frac{x + 3}{5 x}$

$\frac{2 x + 4}{5 x}$

Got questions? Get instant answers now!

$\frac{a - 6}{a + 2} + \frac{a - 2}{a + 2}$

Got questions? Get instant answers now!

$\frac{b + 1}{b - 3} + \frac{b + 2}{b - 3}$

$\frac{2 b + 3}{b - 3}$

Got questions? Get instant answers now!

$\frac{a + 2}{a - 5} - \frac{a + 3}{a - 5}$

Got questions? Get instant answers now!

$\frac{b + 7}{b - 6} - \frac{b - 1}{b - 6}$

$\frac{8}{b - 6}$

Got questions? Get instant answers now!

$\frac{2 b + 3}{b + 1} - \frac{b - 4}{b + 1}$

Got questions? Get instant answers now!

$\frac{3 y + 4}{y + 8} - \frac{2 y - 5}{y + 8}$

$\frac{y + 9}{y + 8}$

Got questions? Get instant answers now!

$\frac{2 a - 7}{a - 9} + \frac{3 a + 5}{a - 9}$

Got questions? Get instant answers now!

$\frac{8 x - 1}{x + 2} - \frac{15 x + 7}{x + 2}$

$\frac{- 7 x - 8}{x + 2}$

Got questions? Get instant answers now!

$\frac{7}{2 x^{2}} + \frac{1}{6 x^{3}}$

Got questions? Get instant answers now!

$\frac{2}{3 x} + \frac{4}{6 x^{2}}$

$\frac{2 (x + 1)}{3 x^{2}}$

Got questions? Get instant answers now!

$\frac{5}{6 y^{3}} - \frac{2}{18 y^{5}}$

Got questions? Get instant answers now!

$\frac{2}{5 a^{2}} - \frac{1}{10 a^{3}}$

$\frac{4 a - 1}{10 a^{3}}$

Got questions? Get instant answers now!

$\frac{3}{x + 1} + \frac{5}{x - 2}$

Got questions? Get instant answers now!

$\frac{4}{x - 6} + \frac{1}{x - 1}$

$\frac{5 (x - 2)}{(x - 6) (x - 1)}$

Got questions? Get instant answers now!

$\frac{2 a}{a + 1} - \frac{3 a}{a + 4}$

Got questions? Get instant answers now!

$\frac{6 y}{y + 4} + \frac{2 y}{y + 3}$

$\frac{2 y (4 y + 13)}{(y + 4) (y + 3)}$

Got questions? Get instant answers now!

$\frac{x - 1}{x - 3} + \frac{x + 4}{x - 4}$

Got questions? Get instant answers now!

$\frac{x + 2}{x - 5} + \frac{x - 1}{x + 2}$

$\frac{2 x^{2} - 2 x + 9}{(x - 5) (x + 2)}$

Got questions? Get instant answers now!

$\frac{a + 3}{a - 3} - \frac{a + 2}{a - 2}$

Got questions? Get instant answers now!

$\frac{y + 1}{y - 1} - \frac{y + 4}{y - 4}$

$\frac{- 6 y}{(y - 1) (y - 4)}$

Got questions? Get instant answers now!

$\frac{x - 1}{(x + 2) (x - 3)} + \frac{x + 4}{x - 3}$

Got questions? Get instant answers now!

$\frac{y + 2}{(y + 1) (y + 6)} + \frac{y - 2}{y + 6}$

$\frac{y^{2}}{(y + 1) (y + 6)}$

Got questions? Get instant answers now!

$\frac{2 a + 1}{(a + 3) (a - 3)} - \frac{a + 2}{a + 3}$

Got questions? Get instant answers now!

$\frac{3 a + 5}{(a + 4) (a - 1)} - \frac{2 a - 1}{a - 1}$

$\frac{- 2 a^{2} - 4 a + 9}{(a + 4) (a - 1)}$

Got questions? Get instant answers now!

$\frac{2 x}{x^{2} - 3 x + 2} + \frac{3}{x - 2}$

Got questions? Get instant answers now!

$\frac{4 a}{a^{2} - 2 a - 3} + \frac{3}{a + 1}$

$\frac{7 a - 9}{(a + 1) (a - 3)}$

Got questions? Get instant answers now!

$\frac{3 y}{y^{2} - 7 y + 12} - \frac{y^{2}}{y - 3}$

Got questions? Get instant answers now!

$\frac{x - 1}{x^{2} + 6 x + 8} + \frac{x + 3}{x^{2} + 2 x - 8}$

$\frac{2 (x^{2} + x + 4)}{(x + 2) (x - 2) (x + 4)}$

Got questions? Get instant answers now!

$\frac{a - 4}{a^{2} + 2 a - 3} + \frac{a + 2}{a^{2} + 3 a - 4}$

Got questions? Get instant answers now!

$\frac{b - 3}{b^{2} + 9 b + 20} + \frac{b + 4}{b^{2} + b - 12}$

$\frac{2 b^{2} + 3 b + 29}{(b - 3) (b + 4) (b + 5)}$

Got questions? Get instant answers now!

$\frac{y - 1}{y^{2} + 4 y - 12} - \frac{y + 3}{y^{2} + 6 y - 16}$

Got questions? Get instant answers now!

$\frac{x + 3}{x^{2} + 9 x + 14} - \frac{x - 5}{x^{2} - 4}$

$\frac{- x + 29}{(x - 2) (x + 2) (x + 7)}$

Got questions? Get instant answers now!

$\frac{x - 1}{x^{2} - 4 x + 3} + \frac{x + 3}{x^{2} - 5 x + 6} + \frac{2 x}{x^{2} - 3 x + 2}$

Got questions? Get instant answers now!

$\frac{4 x}{x^{2} + 6 x + 8} + \frac{3}{x^{2} + x - 6} + \frac{x - 1}{x^{2} + x - 12}$

$\frac{5 x^{4} - 3 x^{3} - 34 x^{2} + 34 x - 60}{(x - 2) (x + 2) (x - 3) (x + 3) (x + 4)}$

Got questions? Get instant answers now!

$\frac{y + 2}{y^{2} - 1} + \frac{y - 3}{y^{2} - 3 y - 4} - \frac{y + 3}{y^{2} - 5 y + 4}$

Got questions? Get instant answers now!

$\frac{a - 2}{a^{2} - 9 a + 18} + \frac{a - 2}{a^{2} - 4 a - 12} - \frac{a - 2}{a^{2} - a - 6}$

$\frac{(a + 5) (a - 2)}{(a + 2) (a - 3) (a - 6)}$

Got questions? Get instant answers now!

$\frac{y - 2}{y^{2} + 6 y} + \frac{y + 4}{y^{2} + 5 y - 6}$

Got questions? Get instant answers now!

$\frac{a + 1}{a^{3} + 3 a^{2}} - \frac{a + 6}{a^{2} - a}$

$\frac{- a^{3} - 8 a^{2} - 18 a - 1}{a^{2} (a + 3) (a - 1)}$

Got questions? Get instant answers now!

$\frac{4}{3 b^{2} - 12 b} - \frac{2}{6 b^{2} - 6 b}$

Got questions? Get instant answers now!

$\frac{3}{2 x^{5} - 4 x^{4}} + \frac{- 2}{8 x^{3} + 24 x^{2}}$

$\frac{- x^{3} + 2 x^{2} + 6 x + 18}{4 x^{4} (x - 2) (x + 3)}$

Got questions? Get instant answers now!

$\frac{x + 2}{12 x^{3}} + \frac{x + 1}{4 x^{2} + 8 x - 12} - \frac{x + 3}{16 x^{2} - 32 x + 16}$

Got questions? Get instant answers now!

$\frac{2 x}{x^{2} - 9} - \frac{x + 1}{4 x^{2} - 12 x} - \frac{x - 4}{8 x^{3}}$

$\frac{14 x^{4} - 9 x^{3} - 2 x^{2} + 9 x - 36}{8 x^{3} (x + 3) (x - 3)}$

Got questions? Get instant answers now!

$4 + \frac{3}{x + 2}$

Got questions? Get instant answers now!

$8 + \frac{2}{x + 6}$

$\frac{8 x + 50}{x + 6}$

Got questions? Get instant answers now!

$1 + \frac{4}{x - 7}$

Got questions? Get instant answers now!

$3 + \frac{5}{x - 6}$

$\frac{3 x - 13}{x - 6}$

Got questions? Get instant answers now!

$- 2 + \frac{4 x}{x + 5}$

Got questions? Get instant answers now!

$- 1 + \frac{3 a}{a - 1}$

$\frac{2 a + 1}{a - 1}$

Got questions? Get instant answers now!

$6 - \frac{4 y}{y + 2}$

Got questions? Get instant answers now!

$2 x + \frac{x^{2} - 4}{x + 1}$

$\frac{3 x^{2} + 2 x - 4}{x + 1}$

Got questions? Get instant answers now!

$- 3 y + \frac{4 y^{2} + 2 y - 5}{y + 3}$

Got questions? Get instant answers now!

$x + 2 + \frac{x^{2} + 4}{x - 1}$

$\frac{2 x^{2} + x + 2}{x - 1}$

Got questions? Get instant answers now!

$b + 6 + \frac{2 b + 5}{b - 2}$

Got questions? Get instant answers now!

$\frac{3 x - 1}{x - 4} - 8$

$\frac{- 5 x + 31}{x - 4}$

Got questions? Get instant answers now!

$\frac{4 y + 5}{y + 1} - 9$

Got questions? Get instant answers now!

$\frac{2 y^{2} + 11 y - 1}{y + 4} - 3 y$

$\frac{- (y^{2} + y + 1)}{y + 4}$

Got questions? Get instant answers now!

$\frac{5 y^{2} - 2 y + 1}{y^{2} + y - 6} - 2$

Got questions? Get instant answers now!

$\frac{4 a^{3} + 2 a^{2} + a - 1}{a^{2} + 11 a + 28} + 3 a$

$\frac{7 a^{3} + 35 a^{2} + 85 a - 1}{(a + 7) (a + 4)}$

Got questions? Get instant answers now!

$\frac{2 x}{1 - x} + \frac{6 x}{x - 1}$

Got questions? Get instant answers now!

$\frac{5 m}{6 - m} + \frac{3 m}{m - 6}$

$\frac{- 2 m}{m - 6}$

Got questions? Get instant answers now!

$\frac{- a + 7}{8 - 3 a} + \frac{2 a + 1}{3 a - 8}$

Got questions? Get instant answers now!

$\frac{- 2 y + 4}{4 - 5 y} - \frac{9}{5 y - 4}$

$\frac{2 y - 13}{5 y - 4}$

Got questions? Get instant answers now!

$\frac{m - 1}{1 - m} - \frac{2}{m - 1}$

Got questions? Get instant answers now!

Exercises for review

( [link] ) Simplify ${(x^{3} y^{2} z^{5})}^{6} {(x^{2} y z)}^{2} .$

$x^{22} y^{14} z^{32}$

Got questions? Get instant answers now!

( [link] ) Write $6 a^{- 3} b^{4} c^{- 2} a^{- 1} b^{- 5} c^{3}$ so that only positive exponents appear.

Got questions? Get instant answers now!

( [link] ) Construct the graph of $y = - 2 x + 4.$
An xy coordinate plane with gridlines, labeled negative five to five on both axes.

A graph of a line passing through three points with coordinates zero, four; one, two; and two, zero.

Got questions? Get instant answers now!

( [link] ) Find the product: $\frac{x^{2} - 3 x - 4}{x^{2} + 6 x + 5} \cdot \frac{x^{2} + 5 x + 6}{x^{2} - 2 x - 8} .$

Got questions? Get instant answers now!

( [link] ) Replace N with the proper quantity: $\frac{x + 3}{x - 5} = \frac{N}{x^{2} - 7 x + 10} .$

$(x + 3) (x - 2)$

Got questions? Get instant answers now!

Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.

Widad Reply

can you send the book attached ?

Ariel

?

Ariel

What is economics

Widad Reply

the study of how humans make choices under conditions of scarcity

AI-Robot

U(x,y) = (x×y)1/2 find mu of x for y

Desalegn Reply

U(x,y) = (xÃy)1/2 find mu of x for y

Desalegn

what is ecnomics

Jan Reply

this is the study of how the society manages it's scarce resources

Belonwu

what is macroeconomic

John Reply

macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.

husaini

etc

husaini

difference between firm and industry

husaini Reply

what's the difference between a firm and an industry

Abdul

firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅

Abdulraufu

Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?

Toofiq Reply

explain standard reason why economic is a science

innocent Reply

factors influencing supply

Petrus Reply

what is economic.

Milan Reply

scares means__________________ends resources. unlimited

Jan

economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses

Jan

calculate the profit maximizing for demand and supply

Zarshad Reply

Why qualify 28 supplies

Milan

what are explicit costs

Nomsa Reply

out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials

AI-Robot

concepts of supply in microeconomics

David Reply

economic overview notes

Amahle Reply

identify a demand and a supply curve

Salome Reply

i don't know

Parul

there's a difference

Aryan

Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods

Israr

Hi Sir please how do u calculate Cross elastic demand and income elastic demand?

Abari

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

1
2
>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

	10 Practice set c By OpenStax Read Online Course
	8 Practice set b By OpenStax Read Online Course
	3 Lec:3 Cohort Studies By Janet Forrester Start Quiz
©flickr: Abraham	1 Biology 1 By Sarah Warren Start Test
	Algebra and trigonometry By OpenStax Read Online Course
	Interventionism Mixed Economy By Robert Murphy Start Test
	How much do you love him? By Zarina Chocolate Start Quiz
	28 AP Key Terms 28 Development Inheritance By OpenStax Start Key Terms
©flickr: U.S.	Biology Chapter 10 By Michael Sag Start Exam
	Microbiology Practice Test By Sandhills MLT Start Test
	Vocabulary for "A Rose for Emily" By Bonnie Hurst Start Quiz
	Interventionism Mixed Economy By Robert Murphy Start Test