### Home > PC3 > Chapter 3 > Lesson 3.1.5 > Problem3-84

3-84.

Rewrite the following fraction as a sum of fractions, with linear denominators, by using partial fraction decomposition.

$\frac { 5 x + 1 } { ( x + 2 ) ( x - 1 ) }$

$\frac{A}{x+2}+\frac{B}{x-1}$

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

$A\left(x-1\right)+B\left(x+2\right)=5x+1$

$Ax-A+Bx+2B=5x+1$

$Ax+Bx=5x\text{ or }A+B=5$
$-A+2B=1$

Solve the system in Step $5$ for $A$ and $B$.