# Multiplying and Dividing Rational Expressions

Multiplying and dividing rational expressions follows the
same format as multiplying and

dividing fractions, the only difference is that you must factor the rational
expressions

before simplifying the common factors.

**Multiplication**

You multiply fractions by multiplying across:
If possible, you can simplify

before multiplying – remember you must simplify in both the numerator and

denominator. For example:

**Example 1:** Multiply the rational expressions, be
sure the answer is simplified:

**Solution:** The first step is to factor everything
completely, then get rid of the common

factors between the numerator and denominator.

**Example 2:** Multiply the rational expressions, be
sure the answer is simplified:

**Solution:**

Note: It is easiest (and best) to leave the answer in
factored form – it is not necessary to

multiply out the denominator.

**Division**

Division of fractions is the same as multiplying the first fraction by the
reciprocal of the

second fraction (always take the reciprocal of the fraction to the right of the
division

symbol).

**Example 3:** Divide – be sure the answer is
simplified:

**Solution:** The first step is to change the division
problem to a multiplication problem.

The next step is to factor everything and multiply.

This section heavily depends on your factoring ability. Be
sure to review your factoring

worksheets, including how to factor the difference of squares and the
sum/difference of

cubes.

**Practice Problems**

Multiply and divide the rational expressions – be sure all
answers are simplified

completely.

Remember order of operations for the last two problems: