Practice Multiplying and Dividing Rational Expressions in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Multiplying rational expressions by multiplying numerators together and denominators together (after factoring and canceling). Dividing by multiplying by the reciprocal of the divisor.

It works exactly like multiplying and dividing numeric fractions. To multiply: factor everything, cancel common factors across any numerator and any denominator, then multiply across. To divide: flip the second fraction and multiply. \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}.

Example 1

medium
Multiply \frac{x^2 - 1}{x + 3} \cdot \frac{x + 3}{x + 1}.

Example 2

hard
Divide \frac{x^2 - 4}{x^2 + x} \div \frac{x - 2}{x}.

Example 3

easy
Multiply \frac{3}{x} \cdot \frac{x^2}{6}.

Example 4

medium
Divide \frac{x + 5}{x - 1} \div \frac{x + 5}{x^2 - 1}.