12.8: Multiplication of Rational Expressions
What if you had two rational expressions like
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CK12 Foundation: 1208S Multiplying Rational Expressions
Guidance
The rules for multiplying and dividing rational expressions are the same as the rules for multiplying and dividing rational numbers, so let’s start by reviewing multiplication and division of fractions. When we multiply two fractions we multiply the numerators and denominators separately:
Multiply Rational Expressions Involving Monomials
Example A
Multiply the following:
Solution
Cancel common factors from the numerator and denominator. The common factors are 4,
Example B
Multiply
Solution
Rewrite the problem as a product of two fractions:
The common factors are 3 and
Multiply Rational Expressions Involving Polynomials
When multiplying rational expressions involving polynomials, first we need to factor all polynomial expressions as much as we can. Then we follow the same procedure as before.
Example C
Multiply
Solution
Factor all polynomial expressions as much as possible:
The common factors are
Multiply a Rational Expression by a Polynomial
When we multiply a rational expression by a whole number or a polynomial, we can write the whole number (or polynomial) as a fraction with denominator equal to one. We then proceed the same way as in the previous examples.
Example D
Multiply
Solution
Rewrite the expression as a product of fractions:
Factor polynomials:
The common factor is
Watch this video for help with the Examples above.
CK12 Foundation: Multiplying Rational Expressions
Vocabulary
 When we multiply two fractions we multiply the numerators and denominators separately:
Guided Practice
Multiply
Solution
Factor polynomials:
The common factors are
Explore More
Multiply the following rational expressions and reduce the answer to lowest terms.

x32y3⋅2y2x 
2xy2⋅4y5x 
2xy⋅2y2x3 
4y2−1y2−9⋅y−32y−1 
6aba2⋅a3b3b2 
33a2−5⋅2011a3 
2x2+2x−24x2+3x⋅x2+x−6x+4 
xx−5⋅x2−8x+15x2−3x 
5x2+16x+336x2−25⋅(6x2+5x) 
x2+7x+10x2−9⋅x2−3x3x2+4x−4 
x2+8x+167x2+9x+2⋅7x+2x2+4x
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Description
Learning Objectives
Here you'll learn how to multiply two monomial rational expressions, two polynomial rational expressions, and a rational expression by a polynomial.
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Date Created:
Oct 01, 2012Last Modified:
Aug 20, 2015Vocabulary
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