Pre-Algebra Examples

$\frac{x + 4}{x^{2} - 4} + \frac{- 2 x - 2}{x^{2} - 4}$

Step 1

Simplify terms.

Tap for more steps...

Step 1.1

Combine the numerators over the common denominator.

$\frac{x + 4 - 2 x - 2}{x^{2} - 4}$

Step 1.2

Subtract

$2 x$ from

$x$ .

$\frac{- x + 4 - 2}{x^{2} - 4}$

Step 1.3

Subtract

$2$ from

$4$ .

$\frac{- x + 2}{x^{2} - 4}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite

$4$ as

$2^{2}$ .

$\frac{- x + 2}{x^{2} - 2^{2}}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula,

$a^{2} - b^{2} = (a + b) (a - b)$ where

$a = x$ and

$b = 2$ .

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

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of

$- x + 2$ and

$x - 2$ .

Tap for more steps...

Step 3.1.1

Factor

$- 1$ out of

$- x$ .

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

Step 3.1.2

Rewrite

$2$ as

$- 1 (- 2)$ .

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

Step 3.1.3

Factor

$- 1$ out of

$- (x) - 1 (- 2)$ .

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

Step 3.1.4

Rewrite

$- (x - 2)$ as

$- 1 (x - 2)$ .

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

Step 3.1.5

Cancel the common factor.

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

Step 3.1.6

Rewrite the expression.

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

Step 3.2

Move the negative in front of the fraction.

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