Practice Adding and Subtracting Rational Expressions in Math

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

Quick Recap

Adding or subtracting rational expressions by finding a least common denominator (LCD), rewriting each fraction with the LCD, then combining the numerators over the common denominator.

Just like \frac{1}{3} + \frac{1}{4} requires a common denominator of 12, adding \frac{2}{x+1} + \frac{3}{x-2} requires the LCD (x+1)(x-2). Rewrite each fraction so both have the same denominator, then add the numerators. The process mirrors numeric fractions but with polynomial denominators.

Example 1

medium
Add \frac{2}{x+1} + \frac{3}{x-2}.

Example 2

hard
Subtract \frac{x}{x+2} - \frac{3}{x^2 + 4x + 4}.

Example 3

easy
Add \frac{3}{x} + \frac{5}{x}.

Example 4

medium
Subtract \frac{5}{x-3} - \frac{2}{x+1}.