Simplify (x^2-81)/(6x^2-54x)

$\frac{x^{2} - 81}{6 x^{2} - 54 x}$

Simplify the numerator.

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

$\frac{x^{2} - 9^{2}}{6 x^{2} - 54 x}$

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 $b = 9$ .

$\frac{(x + 9) (x - 9)}{6 x^{2} - 54 x}$

Simplify terms.

Factor $6 x$ out of $6 x^{2} - 54 x$ .

Factor $6 x$ out of $6 x^{2}$ .

$\frac{(x + 9) (x - 9)}{6 x (x) - 54 x}$

Factor $6 x$ out of $- 54 x$ .

$\frac{(x + 9) (x - 9)}{6 x (x) + 6 x (- 9)}$

Factor $6 x$ out of $6 x (x) + 6 x (- 9)$ .

$\frac{(x + 9) (x - 9)}{6 x (x - 9)}$

Cancel the common factor of $x - 9$ .

Cancel the common factor.

$\frac{(x + 9) (x - 9)}{6 x (x - 9)}$

Rewrite the expression.

$\frac{x + 9}{6 x}$