8.3 Add and subtract rational expressions with a common denominator  (Page 2/2)

$\frac{2}{15}+\frac{7}{15}$

$\frac{4}{21}+\frac{3}{21}$

$\frac{7}{24}+\frac{11}{24}$

$\frac{7}{36}+\frac{13}{36}$

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

$\frac{3c}{4c-5}+\frac{5}{4c-5}$

$\frac{d}{d+8}+\frac{5}{d+8}$

$\frac{7m}{2m+n}+\frac{4}{2m+n}$

$\frac{p^2+10p}{p+2}+\frac{16}{p+2}$

$\frac{q^2+12q}{q+3}+\frac{27}{q+3}$

$\frac{2r^2}{2r-1}+\frac{15r-8}{2r-1}$

$\frac{3s^2}{3s-2}+\frac{13s-10}{3s-2}$

$\frac{8t^2}{t+4}+\frac{32t}{t+4}$

$\frac{6v^2}{v+5}+\frac{30v}{v+5}$

$\frac{2w^2}{w^2-16}+\frac{8w}{w^2-16}$

$\frac{7x^2}{x^2-9}+\frac{21x}{x^2-9}$

$\frac{y^2}{y+8}-\frac{64}{y+8}$

$\frac{z^2}{z+2}-\frac{4}{z+2}$

$\frac{9a^2}{3a-7}-\frac{49}{3a-7}$

$\frac{25b^2}{5b-6}-\frac{36}{5b-6}$

$\frac{c^2}{c-8}-\frac{6c+16}{c-8}$

$\frac{d^2}{d-9}-\frac{6d+27}{d-9}$

$\frac{3m^2}{6m-30}-\frac{21m-30}{6m-30}$

$\frac{2n^2}{4n-32}-\frac{30n-16}{4n-32}$

$\frac{6p^2+3p+4}{p^2+4p-5}-\frac{5p^2+p+7}{p^2+4p-5}$

$\frac{5q^2+3q-9}{q^2+6q+8}-\frac{4q^2+9q+7}{q^2+6q+8}$

$\frac{5r^2+7r-33}{r^2-49}-\frac{4r^2-5r-30}{r^2-49}$

$\frac{7t^2-t-4}{t^2-25}-\frac{6t^2+2t-1}{t^2-25}$

$\frac{10v}{2v-1}+\frac{2v+4}{1-2v}$

$\frac{20w}{5w-2}+\frac{5w+6}{2-5w}$

$\frac{10x^2+16x-7}{8x-3}+\frac{2x^2+3x-1}{3-8x}$

$\frac{6y^2+2y-11}{3y-7}+\frac{3y^2-3y+17}{7-3y}$

$\frac{z^2+6z}{z^2-25}-\frac{3z+20}{25-z^2}$

$\frac{a^2+3a}{a^2-9}-\frac{3a-27}{9-a^2}$

$\frac{2b^2+30b-13}{b^2-49}-\frac{2b^2-5b-8}{49-b^2}$

$\frac{c^2+5c-10}{c^2-16}-\frac{c^2-8c-10}{16-c^2}$

Sarah ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. If $r$ represents Sarah’s speed when she ran, then her running time is modeled by the expression $\frac{8}{r}$ and her biking time is modeled by the expression $\frac{24}{r+4}.$ Add the rational expressions $\frac{8}{r}+\frac{24}{r+4}$ to get an expression for the total amount of time Sarah ran and biked.

If Pete can paint a wall in $p$ hours, then in one hour he can paint $\frac{1}{p}$ of the wall. It would take Penelope 3 hours longer than Pete to paint the wall, so in one hour she can paint $\frac{1}{p+3}$ of the wall. Add the rational expressions $\frac{1}{p}+\frac{1}{p+3}$ to get an expression for the part of the wall Pete and Penelope would paint in one hour if they worked together.

Donald thinks that $\frac{3}{x}+\frac{4}{x}$ is $\frac{7}{2x}.$ Is Donald correct? Explain.

Explain how you find the Least Common Denominator of $x^2+5x+4$ and $x^2-16.$