Below is a set of practice problems on decomposing rational expressions into partial fractions. The complete answers are provided at the bottom of the page.
For a detailed explanation of the method, see this reference on partial fractions .
Decompose into partial fractions:
\[ \frac{5x + 10}{x(x + 5)} \]Decompose into partial fractions:
\[ \frac{8x + 14}{(x + 1)(x + 5)} \]Decompose into partial fractions:
\[ \frac{5x^2 + 12x + 3}{x(x + 1)^2} \]Decompose into partial fractions:
\[ \frac{3x + 15}{(x + 4)^2} \]Decompose into partial fractions:
\[ \frac{7x + 10}{(x + 1)(x^2 - 4)} \]Decompose into partial fractions:
\[ \frac{5x^2 + 31x + 46}{(x + 2)(x + 3)^2} \]Decompose into partial fractions:
\[ \frac{2x^2 + 6x - 2}{x^3 - 1} \]1)
\[ \frac{2}{x} + \frac{3}{x + 5} \]2)
\[ \frac{3}{2(x + 1)} + \frac{13}{2(x + 5)} \]3)
\[ \frac{3}{x} + \frac{2}{x + 1} + \frac{4}{(x + 1)^2} \]4)
\[ \frac{3}{x + 4} + \frac{3}{(x + 4)^2} \]5)
\[ \frac{2}{x - 2} - \frac{1}{x + 2} - \frac{1}{x + 1} \]6)
\[ \frac{4}{x + 2} + \frac{1}{x + 3} + \frac{2}{(x + 3)^2} \]7)
\[ \frac{2}{x - 1} + \frac{4}{x^2 + x + 1} \]