Practice Solving Rational Equations in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Solving equations that contain rational expressions by multiplying every term by the LCD to clear all denominators, solving the resulting polynomial equation, and checking for extraneous solutions.

Fractions make equations messy. Multiply every term by the LCD to 'clear' all the denominators at once, turning a rational equation into a simpler polynomial equation. But be careful—values that make any original denominator zero are excluded from the domain and must be rejected even if they appear as solutions.

Showing a random 20 of 50 problems.

Example 1

medium
Solve x+2x=32\frac{x+2}{x} = \frac{3}{2}.

Example 2

easy
Solve 3x+2=1\frac{3}{x+2} = 1.

Example 3

medium
Solve 2x−1=4x+3\frac{2}{x-1} = \frac{4}{x+3}.

Example 4

challenge
Solve 1x+1x+2=12\frac{1}{x} + \frac{1}{x+2} = \frac{1}{2} for the positive root.

Example 5

easy
Solve 12x=3\frac{12}{x} = 3.

Example 6

hard
Solve 6x−1=x+4\frac{6}{x-1} = x + 4.

Example 7

easy
Solve 6x=2\frac{6}{x} = 2.

Example 8

medium
Solve 3x=x3\frac{3}{x} = \frac{x}{3}.

Example 9

easy
Find the LCD of 1x−2\frac{1}{x-2} and 3x+5\frac{3}{x+5}.

Example 10

medium
Solve xx+3=4x+3\frac{x}{x+3} = \frac{4}{x+3}.

Example 11

easy
Solve x3=4\frac{x}{3} = 4.

Example 12

medium
Solve 1x−1x+1=112\frac{1}{x} - \frac{1}{x+1} = \frac{1}{12} for the positive root.

Example 13

challenge
Solve 1x+1x−1+1x+1=0\frac{1}{x} + \frac{1}{x-1} + \frac{1}{x+1} = 0.

Example 14

medium
Solve 1x+12=1\frac{1}{x} + \frac{1}{2} = 1.

Example 15

medium
Solve 3x+12=5x\frac{3}{x} + \frac{1}{2} = \frac{5}{x}.

Example 16

easy
What value of xx must be excluded from 5x−2\frac{5}{x-2}?

Example 17

medium
Solve x2+x3=5\frac{x}{2} + \frac{x}{3} = 5.

Example 18

medium
What is the LCD of 1x2−4\frac{1}{x^2-4} and 1x+2\frac{1}{x+2}?

Example 19

challenge
Solve xx−3+3x−3=2\frac{x}{x-3} + \frac{3}{x-3} = 2.

Example 20

easy
After solving a rational equation, what must you always do before declaring victory?
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