Practice Partial Fraction Decomposition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A technique for breaking a rational expression \frac{P(x)}{Q(x)} into a sum of simpler fractions whose denominators are the factors of Q(x). This makes integration of rational functions possible.
Just as \frac{7}{12} can be split into \frac{1}{3} + \frac{1}{4}, a complex fraction like \frac{5x-1}{(x+1)(x-2)} can be split into \frac{A}{x+1} + \frac{B}{x-2}. The simpler pieces are each easy to integrate.
Example 1
easyDecompose \dfrac{5}{(x+1)(x-2)} and integrate.
Example 2
hardIntegrate \displaystyle\int \frac{x^2+2x-1}{x(x-1)^2}\,dx.
Example 3
easyDecompose \dfrac{3x+5}{(x+1)(x+2)}.
Example 4
mediumIntegrate \displaystyle\int \frac{1}{x^2-4}\,dx.