Practice Solving Rational Equations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
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.
Example 1
mediumSolve \frac{3}{x} + \frac{1}{2} = \frac{5}{x}.
Example 2
hardSolve \frac{x}{x-2} - \frac{1}{x+1} = \frac{3}{(x-2)(x+1)}.
Example 3
easySolve \frac{10}{x} = 5.
Example 4
mediumSolve \frac{2}{x-1} = \frac{4}{x+3}.