Simplify ((x^2-4)/(16-x^2))((16-4x)/(4x+8))

$(\frac{x^{2} - 4}{16 - x^{2}}) (\frac{16 - 4 x}{4 x + 8})$

Step 1

Simplify the numerator.

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

$\frac{x^{2} - 2^{2}}{16 - x^{2}} \cdot \frac{16 - 4 x}{4 x + 8}$

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 $b = 2$ .

$\frac{(x + 2) (x - 2)}{16 - x^{2}} \cdot \frac{16 - 4 x}{4 x + 8}$

Step 2

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{(x + 2) (x - 2)}{4^{2} - x^{2}} \cdot \frac{16 - 4 x}{4 x + 8}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = x$ .

$\frac{(x + 2) (x - 2)}{(4 + x) (4 - x)} \cdot \frac{16 - 4 x}{4 x + 8}$

Step 3

Simplify terms.

Factor $4$ out of $16 - 4 x$ .

Factor $4$ out of $16$ .

$\frac{(x + 2) (x - 2)}{(4 + x) (4 - x)} \cdot \frac{4 (4) - 4 x}{4 x + 8}$

Factor $4$ out of $- 4 x$ .

$\frac{(x + 2) (x - 2)}{(4 + x) (4 - x)} \cdot \frac{4 (4) + 4 (- x)}{4 x + 8}$

Factor $4$ out of $4 (4) + 4 (- x)$ .

$\frac{(x + 2) (x - 2)}{(4 + x) (4 - x)} \cdot \frac{4 (4 - x)}{4 x + 8}$

Factor $4$ out of $4 x + 8$ .

Factor $4$ out of $4 x$ .

$\frac{(x + 2) (x - 2)}{(4 + x) (4 - x)} \cdot \frac{4 (4 - x)}{4 (x) + 8}$

Factor $4$ out of $8$ .

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

Factor $4$ out of $4 x + 4 \cdot 2$ .

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

Cancel the common factor of $x + 2$ .

Factor $x + 2$ out of $4 (x + 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4 - x$ .

Factor $4 - x$ out of $(4 + x) (4 - x)$ .

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

Factor $4 - x$ out of $4 (4 - x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{x - 2}{4 + x}$ by $\frac{4}{4}$ .

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((x^2-4)/(16-x^2))((16-4x)/(4x+8))

Related Questions

Support LCMGCF.com by disabling your adblocker.