# How do you use partial fraction decomposition to decompose the fraction to integrate (3x)/((x + 2)(x - 1))?

May 11, 2018

The required format in partial fraction is$\frac{2}{x + 2} + \frac{1}{x - 1}$

#### Explanation:

Let us consider two constants A and B such that $\frac{A}{x + 2} + \frac{B}{x - 1}$
Now taking L.C.M we get
$\frac{A \left(x - 1\right) + B \left(x + 2\right)}{\left(x - 1\right) \left(x + 2\right)} = 3 \frac{x}{\left(x + 2\right) \left(x - 1\right)}$
Comparing the numerators we get
$\left(A \left(x - 1\right) + B \left(x + 2\right)\right) = 3 x$
Now putting x=1 we get
B=1
And putting x=-2 we get
A=2
So required form is
$\frac{2}{x + 2} + \frac{1}{x - 1}$

Hope it helps!!