Simplify ((x^2-16)/(x-2))÷((x^2+3x-4)/(x-8))

$\frac{x^{2} - 16}{x - 2} \div \frac{x^{2} + 3 x - 4}{x - 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 16}{x - 2} \cdot \frac{x - 8}{x^{2} + 3 x - 4}$

Step 2

Simplify the numerator.

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

$\frac{x^{2} - 4^{2}}{x - 2} \cdot \frac{x - 8}{x^{2} + 3 x - 4}$

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 $b = 4$ .

$\frac{(x + 4) (x - 4)}{x - 2} \cdot \frac{x - 8}{x^{2} + 3 x - 4}$

Step 3

Factor $x^{2} + 3 x - 4$ 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 $- 4$ and whose sum is $3$ .

$- 1, 4$

Write the factored form using these integers.

$\frac{(x + 4) (x - 4)}{x - 2} \cdot \frac{x - 8}{(x - 1) (x + 4)}$

Step 4

Simplify terms.

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $(x - 1) (x + 4)$ .

$\frac{(x + 4) (x - 4)}{x - 2} \cdot \frac{x - 8}{(x + 4) (x - 1)}$

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{x - 2} \cdot \frac{x - 8}{(x + 4) (x - 1)}$

Rewrite the expression.

$\frac{x - 4}{x - 2} \cdot \frac{x - 8}{x - 1}$

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

$\frac{(x - 4) (x - 8)}{(x - 2) (x - 1)}$

Simplify ((x^2-16)/(x-2))÷((x^2+3x-4)/(x-8))

Related Questions

Support LCMGCF.com by disabling your adblocker.