Simplify (-4x^2+16)/(2x^2+2x-12)

$\frac{- 4 x^{2} + 16}{2 x^{2} + 2 x - 12}$

Cancel the common factor of $- 4 x^{2} + 16$ and $2 x^{2} + 2 x - 12$ .

Factor $2$ out of $- 4 x^{2}$ .

$\frac{2 (- 2 x^{2}) + 16}{2 x^{2} + 2 x - 12}$

Factor $2$ out of $16$ .

$\frac{2 (- 2 x^{2}) + 2 \cdot 8}{2 x^{2} + 2 x - 12}$

Factor $2$ out of $2 (- 2 x^{2}) + 2 (8)$ .

$\frac{2 (- 2 x^{2} + 8)}{2 x^{2} + 2 x - 12}$

Cancel the common factors.

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (- 2 x^{2} + 8)}{2 (x^{2}) + 2 x - 12}$

Factor $2$ out of $2 x$ .

$\frac{2 (- 2 x^{2} + 8)}{2 (x^{2}) + 2 (x) - 12}$

Factor $2$ out of $2 (x^{2}) + 2 (x)$ .

$\frac{2 (- 2 x^{2} + 8)}{2 (x^{2} + x) - 12}$

Factor $2$ out of $- 12$ .

$\frac{2 (- 2 x^{2} + 8)}{2 (x^{2} + x) + 2 (- 6)}$

Factor $2$ out of $2 (x^{2} + x) + 2 (- 6)$ .

$\frac{2 (- 2 x^{2} + 8)}{2 (x^{2} + x - 6)}$

Cancel the common factor.

$\frac{2 (- 2 x^{2} + 8)}{2 (x^{2} + x - 6)}$

Rewrite the expression.

$\frac{- 2 x^{2} + 8}{x^{2} + x - 6}$

Simplify the numerator.

Factor $2$ out of $- 2 x^{2} + 8$ .

Factor $2$ out of $- 2 x^{2}$ .

$\frac{2 (- x^{2}) + 8}{x^{2} + x - 6}$

Factor $2$ out of $8$ .

$\frac{2 (- x^{2}) + 2 (4)}{x^{2} + x - 6}$

Factor $2$ out of $2 (- x^{2}) + 2 (4)$ .

$\frac{2 (- x^{2} + 4)}{x^{2} + x - 6}$

Rewrite $4$ as $2^{2}$ .

$\frac{2 (- x^{2} + 2^{2})}{x^{2} + x - 6}$

Reorder $- x^{2}$ and $2^{2}$ .

$\frac{2 (2^{2} - x^{2})}{x^{2} + x - 6}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

$\frac{2 (2 + x) (2 - x)}{x^{2} + x - 6}$

Factor $x^{2} + x - 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $1$ .

$- 2, 3$

Write the factored form using these integers.

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2 - x$ and $x - 2$ .

Rewrite $2$ as $- 1 (- 2)$ .

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

Factor $- 1$ out of $- x$ .

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

Factor $- 1$ out of $- 1 (- 2) - (x)$ .

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

Multiply $- 1$ by $2$ .

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

Move the negative in front of the fraction.

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

Simplify (-4x^2+16)/(2x^2+2x-12)

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