Chapter 6.2: Multiplication and Division of Rational Expressions
Multiplying and dividing rational expressions is very similar to the process used to multiply and divide fractions.
Example 1
Reduce and multiply and .
(15 and 45 reduce to 1 and 3, and 14 and 49 reduce to 2 and 7)
This process of multiplication is identical to division, except the first step is to reciprocate any fraction that is being divided.
Example 2
Reduce and divide by .
(25 and 15 reduce to 5 and 3, and 6 and 18 reduce to 1 and 3)
When multiplying with rational expressions, follow the same process: first, divide out common factors, then multiply straight across.
Example 3
Reduce and multiply and .
(25 and 55 reduce to 5 and 11, 24 and 9 reduce to 8 and 3, x2 and x7 reduce to x5, y4 and y8 reduce to y4)
Remember: when dividing fractions, reciprocate the dividing fraction.
Example 4
Reduce and divide by .
(After reciprocating, 4a4b2 and b4 reduce to 4a3 and b2)
In dividing or multiplying some fractions, the polynomials in the fractions must be factored first.
Example 5
Reduce, factor and multiply and .
Dividing or cancelling out the common factors and leaves us with , which results in .
Example 6
Reduce, factor and multiply or divide the following fractions:
Factoring each fraction and reciprocating the last one yields:
Dividing or cancelling out the common polynomials leaves us with:
Questions
Simplify each expression.
Answers to odd questions
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