CPM Homework Help : INT3 Problem 11-57

Add or subtract the following rational expressions. Be sure to look for factors before trying to determine a common denominator, and simplify your answers, if possible.

$\frac { 4 x } { x ^ { 2 } - 2 x - 8 } + \frac { 4 } { x - 4 }$
Hint (a):
This is addition of fractions. What are the steps for adding fractions?
Step 1(a):
Factor.
$\frac{4x}{(x+2)(x-4)}+\frac{4}{x-4}$
Step 2(a):
To make common denominators, multiply the second term by the Giant One below.
$\frac{4x}{(x+2)(x-4)}+\frac{4(x+2)}{(x+2)(x-4)}$
Step 3(a):
Add the numerators and keep the denominators the same.
Answer (a):
$\frac{8x+8}{(x+2)(x-4)}$

$\frac { 16 x - 12 } { 4 x ^ { 2 } + 5 x - 6 } - \frac { 3 } { x + 2 }$
Hint (b):
Refer to part (a).
Answer (b):
$\frac{1}{x+2}$