### Home > CCA2 > Chapter Ch3 > Lesson 3.2.5 > Problem3-120

3-120.

Simplify each expression. Homework Help ✎

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

Begin by factoring $x^2−4$.

Multiply the first term by a Giant One that will make the two denominators the same.

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

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

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

Factor both denominators.

Refer to part (a).

1. $\frac { x ^ { 2 } + 5 x + 6 } { x ^ { 2 } - 9 } \cdot \frac { x - 3 } { x ^ { 2 } + 2 x }$

Factor all parts of the problem that can be factored. Remove Giant Ones.

$\frac{1}{x}$

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

Remove Giant Ones.

$\text{What's }\frac{2-x}{x-2}?$

If you aren't sure, substitute different numbers for $x$.

$\frac{4}{x-2} \cdot \frac{2-x}{8}$

$\frac{4}{8} \cdot \frac{2-x}{x-2}$

$\frac{1}{2}\cdot -1$