Simplify (x^2-81)/(x^2-5x-36)*(x+4)/x

$\frac{x^{2} - 81}{x^{2} - 5 x - 36} \cdot \frac{x + 4}{x}$

Step 1

Simplify the numerator.

Rewrite $81$ as $9^{2}$ .

$\frac{x^{2} - 9^{2}}{x^{2} - 5 x - 36} \cdot \frac{x + 4}{x}$

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 $b = 9$ .

$\frac{(x + 9) (x - 9)}{x^{2} - 5 x - 36} \cdot \frac{x + 4}{x}$

Step 2

Factor $x^{2} - 5 x - 36$ 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 $- 36$ and whose sum is $- 5$ .

$- 9, 4$

Write the factored form using these integers.

$\frac{(x + 9) (x - 9)}{(x - 9) (x + 4)} \cdot \frac{x + 4}{x}$

Step 3

Simplify terms.

Cancel the common factor of $x + 4$ .

Factor $x + 4$ out of $(x - 9) (x + 4)$ .

$\frac{(x + 9) (x - 9)}{(x + 4) (x - 9)} \cdot \frac{x + 4}{x}$

Cancel the common factor.

$\frac{(x + 9) (x - 9)}{(x + 4) (x - 9)} \cdot \frac{x + 4}{x}$

Rewrite the expression.

$\frac{(x + 9) (x - 9)}{x - 9} \cdot \frac{1}{x}$

Multiply $\frac{(x + 9) (x - 9)}{x - 9}$ by $\frac{1}{x}$ .

$\frac{(x + 9) (x - 9)}{(x - 9) x}$

Cancel the common factor of $x - 9$ .

Cancel the common factor.

$\frac{(x + 9) (x - 9)}{(x - 9) x}$

Rewrite the expression.

$\frac{x + 9}{x}$

Simplify (x^2-81)/(x^2-5x-36)*(x+4)/x

Related Questions

Support LCMGCF.com by disabling your adblocker.