Home
College algebra
Prerequisites
Rational expressions
How To
Given a complex rational expression, simplify it.
Combine the expressions in the numerator into a single rational expression by adding or subtracting.
Combine the expressions in the denominator into a single rational expression by adding or subtracting.
Rewrite as the numerator divided by the denominator.
Rewrite as multiplication.
Multiply.
Simplify.
Simplifying complex rational expressions
Simplify:
y
+
1
x
x
y .
Begin by combining the expressions in the numerator into one expression.
y
⋅
x
x
+
1
x
Multiply by
x
x
to get LCD as denominator
.
x
y
x
+
1
x
x
y
+
1
x
Add numerators
.
Now the numerator is a single rational expression and the denominator is a single rational expression.
x
y
+
1
x
x
y
We can rewrite this as division, and then multiplication.
x
y
+
1
x
÷
x
y
x
y
+
1
x
⋅
y
x
Rewrite as multiplication
.
y
(
x
y
+
1
)
x
2
Multiply
.
Got questions? Get instant answers now! Got questions? Get instant answers now!
Q&A
Can a complex rational expression always be simplified?
Yes. We can always rewrite a complex rational expression as a simplified rational expression.
Key concepts
Rational expressions can be simplified by cancelling common factors in the numerator and denominator. See
[link] .
We can multiply rational expressions by multiplying the numerators and multiplying the denominators. See
[link] .
To divide rational expressions, multiply by the reciprocal of the second expression. See
[link] .
Adding or subtracting rational expressions requires finding a common denominator. See
[link] and
[link] .
Complex rational expressions have fractions in the numerator or the denominator. These expressions can be simplified. See
[link] .
Section exercises
Verbal
How can you use factoring to simplify rational expressions?
You can factor the numerator and denominator to see if any of the terms can cancel one another out.
Got questions? Get instant answers now!
Tell whether the following statement is true or false and explain why: You only need to find the LCD when adding or subtracting rational expressions.
True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.
Got questions? Get instant answers now!
Algebraic
For the following exercises, simplify the rational expressions.
For the following exercises, multiply the rational expressions and express the product in simplest form.
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
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
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
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?
explain standard reason why economic is a science
factors influencing supply
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
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
identify a demand and a supply curve
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!
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.