Simplify (8x)/(9x-81)*(x^2-81)/(x^2+x-72)

$\frac{8 x}{9 x - 81} \cdot \frac{x^{2} - 81}{x^{2} + x - 72}$

Factor $9$ out of $9 x - 81$ .

Factor $9$ out of $9 x$ .

$\frac{8 x}{9 (x) - 81} \cdot \frac{x^{2} - 81}{x^{2} + x - 72}$

Factor $9$ out of $- 81$ .

$\frac{8 x}{9 x + 9 \cdot - 9} \cdot \frac{x^{2} - 81}{x^{2} + x - 72}$

Factor $9$ out of $9 x + 9 \cdot - 9$ .

$\frac{8 x}{9 (x - 9)} \cdot \frac{x^{2} - 81}{x^{2} + x - 72}$

Simplify the numerator.

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

$\frac{8 x}{9 (x - 9)} \cdot \frac{x^{2} - 9^{2}}{x^{2} + x - 72}$

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 $b = 9$ .

$\frac{8 x}{9 (x - 9)} \cdot \frac{(x + 9) (x - 9)}{x^{2} + x - 72}$

Factor $x^{2} + x - 72$ 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 $- 72$ and whose sum is $1$ .

$- 8, 9$

Write the factored form using these integers.

$\frac{8 x}{9 (x - 9)} \cdot \frac{(x + 9) (x - 9)}{(x - 8) (x + 9)}$

Simplify terms.

Cancel the common factor of $x - 9$ .

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

$\frac{8 x}{(x - 9) \cdot 9} \cdot \frac{(x + 9) (x - 9)}{(x - 8) (x + 9)}$

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

$\frac{8 x}{(x - 9) \cdot 9} \cdot \frac{(x - 9) (x + 9)}{(x - 8) (x + 9)}$

Cancel the common factor.

$\frac{8 x}{(x - 9) \cdot 9} \cdot \frac{(x - 9) (x + 9)}{(x - 8) (x + 9)}$

Rewrite the expression.

$\frac{8 x}{9} \cdot \frac{x + 9}{(x - 8) (x + 9)}$

Multiply $\frac{8 x}{9}$ by $\frac{x + 9}{(x - 8) (x + 9)}$ .

$\frac{8 x (x + 9)}{9 ((x - 8) (x + 9))}$

Cancel the common factor of $x + 9$ .

Cancel the common factor.

$\frac{8 x (x + 9)}{9 ((x - 8) (x + 9))}$

Rewrite the expression.

$\frac{8 x}{9 (x - 8)}$

Simplify (8x)/(9x-81)*(x^2-81)/(x^2+x-72)

Related Questions

Support LCMGCF.com by disabling your adblocker.