# 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, x^{2} and x^{7} reduce to x^{5}, y^{4} and y^{8} reduce to y^{4})

Remember: when dividing fractions, reciprocate the dividing fraction.

Example 4

Reduce and divide by .

(After reciprocating, 4a^{4}b^{2} and b^{4} reduce to 4a^{3} and b^{2})

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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