### Home > INT3 > Chapter 11 > Lesson 11.2.4 > Problem11-109

11-109.

For each of the following rational expressions, add or subtract, then simplify.

1. $\frac { 2 - x } { x + 4 } + \frac { 3 x + 6 } { x + 4 }$

The denominators are the same, so just add the numerators.

$\frac{ 2x+8 }{x+4 }$

Factor the numerator and look for a Giant One.

$2$

1. $\frac { 3 } { ( x + 2 ) ( x + 3 ) } + \frac { x } { ( x + 2 ) ( x + 3 ) }$

See part (a).

1. $\frac { 3 } { x - 1 } - \frac { 2 } { x - 2 }$

The product of the two denominators is the common denominator. Multiply each term by a Giant One to make the denominators the same.

$\left( \frac{x-2}{x-2} \right) \cdot \left( \frac{3}{x-1}\right) -\left( \frac{2}{x-2}\right)·\left( \frac{x-1}{x-1}\right)$

Distribute:

$\frac{(3x-6)}{(x-2)(x-1)}-\frac{(2x -2)}{(x-2)(x-1)}$

Now, subtract. Notice you are subtracting a negative $2$ in the second term.

$\frac{x-4}{(x-2)(x-1)}$

1. $\frac { 8 } { x } - \frac { 4 } { x + 2 }$

See part (c).