# How do you write (3x)/((x + 2)(x - 1)) as a partial fraction decomposition?

##### 1 Answer
Aug 4, 2016

$= \frac{2}{x + 2} + \frac{1}{x - 1}$

#### Explanation:

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

Getting every term over common denominator yields:

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

When I do these I eliminate one bracket by setting x to a particular value, but there are many other methods.

$\textcolor{red}{x = 1 :}$

$3 = 3 B \implies B = 1$

$\textcolor{red}{x = - 2 :}$

$- 6 = - 3 A \implies A = 2$

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