Practice Simplifying Rational Expressions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Simplifying a rational expression \frac{p(x)}{q(x)} by factoring both the numerator and denominator, then canceling common factors. The domain must exclude values that make any original denominator zero.
Just like simplifying the fraction \frac{6}{8} = \frac{3}{4} by canceling the common factor of 2, you can simplify \frac{x^2 - 4}{x - 2} by factoring the top as (x+2)(x-2) and canceling the common (x-2) factor. But remember: you can only cancel FACTORS (things being multiplied), not TERMS (things being added).
Example 1
mediumSimplify \frac{x^2 - 9}{x^2 + 5x + 6}.
Example 2
easySimplify \frac{4x^2}{2x}.
Example 3
easySimplify \frac{x^2 - 4}{x + 2}.
Example 4
hardSimplify \frac{2x^2 + 5x - 3}{x^2 + 4x + 3}.