CPM Homework Help : PC3 Problem 9-122

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

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

Step 1:

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

Step 2:

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

Step 3:

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

Step 4:

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