# How do you express (3x)/((x + 2)(x - 1)) in partial fractions?

Aug 10, 2016

$\frac{3 x}{\left(x + 2\right) \left(x - 1\right)} = \frac{2}{x + 2} + \frac{1}{x - 1}$

#### Explanation:

$\frac{3 x}{\left(x + 2\right) \left(x - 1\right)} = \frac{A}{x + 2} + \frac{B}{x - 1}$

Use Heaviside's cover-up method to find:

$A = \frac{3 \left(- 2\right)}{\left(- 2\right) - 1} = \frac{- 6}{- 3} = 2$

$B = \frac{3 \left(1\right)}{\left(1\right) + 2} = \frac{3}{3} = 1$

So:

$\frac{3 x}{\left(x + 2\right) \left(x - 1\right)} = \frac{2}{x + 2} + \frac{1}{x - 1}$