### Home > PC3 > Chapter 9 > Lesson 9.2.2 > Problem9-122

9-122.

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

$\frac { 5 x + 3 } { x ^ { 2 } - 1 }$

$\frac{5x+3}{(x+1)(x-1)}$

$\frac{A}{(x+1)}+\frac{B}{(x-1)}=\frac{5x+3}{(x+1)(x-1)}$

$\frac{A}{(x+1)}\cdot\frac{x-1}{(x-1)}+\frac{x+1}{(x+1)}=\frac{5x+3}{(x+1)(x-1)}$

$A(x-1)+B(x+1)=5x+3$