CPM Homework Help : PC3 Problem 13-132

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

$\frac { - 20 x + 61 } { - 3 x ^ { 2 } + 17 x - 10 }$

Step (1):

$\frac { 20 x - 61 } { 3 x ^ { 2 } - 17 x + 10 }$

Step (2):

$\frac { 20 x - 61 } { (3 x -2)(x-5) }$

Step (3):

$\frac{A}{3x-2}+\frac{B}{x-5}=\frac{20x-61}{(3x-2)(x-5)}$

Step (4):

$\frac{A(x-5)}{(3x-2)(x-5)}+\frac{B(3x-2)}{(x-5)(3x-2)}=\frac{20x-61}{(3x-2)(x-5)}$