Adding and Subtracting Rational Expressions Worksheet with Answer Key

What's on the worksheet

1. Find the least common denominator of each pair of fractions, in factored form.
   \dfrac{1}{15p^2q^3} and \dfrac{1}{12p^4q}\dfrac{1}{x^3 - x} and \dfrac{1}{x^2 + 2x + 1}\dfrac{1}{2x + 4}, \dfrac{1}{x^2 - 4} and \dfrac{1}{3x - 6}
2. Simplify each sum or difference and state the excluded values.
   \dfrac{3}{4xy} - \dfrac{5}{6x^2}\dfrac{x}{(x - 3)^2} - \dfrac{1}{x - 3}\dfrac{2x}{x^2 - 1} + \dfrac{1}{x + 1} - \dfrac{1}{x - 1}\dfrac{3}{x^2 - 5x} + \dfrac{6}{25 - x^2}
3. Simplify each complex fraction and state the excluded values.
   \dfrac{\frac{1}{x - 1} + \frac{1}{x + 1}}{\frac{x}{x^2 - 1}}1 + \dfrac{1}{1 + \frac{1}{x}}\dfrac{\frac{x + 1}{x - 1} - \frac{x - 1}{x + 1}}{x^2 + x}
4. Write an expression with a fraction as a single fraction and state the excluded value.
5. Test each student's answer at a given value, find the mistake and correct it.
6. Word problem: Grace's total riding time to a lake and back against the wind.