Multiplying & Dividing Rational Expressions

Two rational expressions can be multiplied or divided just like two rational numbers.

You can use two methods to multiply rational numbers.

Method 1: Multiply numerators and multiply denominators. Then divide each numerator and denominator by the greatest common factor.

Method 2: Divide numerators and denominators by any common factors. Then multiply numerators and denominators.

Steps to multiply two rational expressions:

Step 1: Cancel numerator to denominator if possible (don't cancel parts of a binomial or trinomial)

Step 2: Factor the numerators and denominators if possible.

Step 3: Multiply straight across - remember, you don't need a common denominator to multiply fractions (or rational expressions).

Step1: Change division to multiplication by inverting the divisor (second rational expression)

Step 2: Cross out the common factors (Do not attempt to cancel factors before it is written as a multiplication)

Step 3: Multiply the numerator by the numerator and the denominator by the denominator.

To know about multiplying and dividing rational expressions, read the explanation below.

Practice: Multiply and divide rational expressions in the following exercises.