Simplify (x^2-9)/(x^2+3x-18)*(x+6)/(x-5)

$\frac{x^{2} - 9}{x^{2} + 3 x - 18} \cdot \frac{x + 6}{x - 5}$

Step 1

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{x^{2} - 3^{2}}{x^{2} + 3 x - 18} \cdot \frac{x + 6}{x - 5}$

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 $b = 3$ .

$\frac{(x + 3) (x - 3)}{x^{2} + 3 x - 18} \cdot \frac{x + 6}{x - 5}$

Step 2

Factor $x^{2} + 3 x - 18$ 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 $- 18$ and whose sum is $3$ .

$- 3, 6$

Write the factored form using these integers.

$\frac{(x + 3) (x - 3)}{(x - 3) (x + 6)} \cdot \frac{x + 6}{x - 5}$

Step 3

Simplify terms.

Cancel the common factor of $x + 6$ .

Factor $x + 6$ out of $(x - 3) (x + 6)$ .

$\frac{(x + 3) (x - 3)}{(x + 6) (x - 3)} \cdot \frac{x + 6}{x - 5}$

Cancel the common factor.

$\frac{(x + 3) (x - 3)}{(x + 6) (x - 3)} \cdot \frac{x + 6}{x - 5}$

Rewrite the expression.

$\frac{(x + 3) (x - 3)}{x - 3} \cdot \frac{1}{x - 5}$

Multiply $\frac{(x + 3) (x - 3)}{x - 3}$ by $\frac{1}{x - 5}$ .

$\frac{(x + 3) (x - 3)}{(x - 3) (x - 5)}$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{(x + 3) (x - 3)}{(x - 3) (x - 5)}$

Rewrite the expression.

$\frac{x + 3}{x - 5}$

Simplify (x^2-9)/(x^2+3x-18)*(x+6)/(x-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.