Simplify (x^2-36)/(7x^2-42x)

$\frac{x^{2} - 36}{7 x^{2} - 42 x}$

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$\frac{x^{2} - 6^{2}}{7 x^{2} - 42 x}$

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 $b = 6$ .

$\frac{(x + 6) (x - 6)}{7 x^{2} - 42 x}$

Simplify terms.

Factor $7 x$ out of $7 x^{2} - 42 x$ .

Factor $7 x$ out of $7 x^{2}$ .

$\frac{(x + 6) (x - 6)}{7 x (x) - 42 x}$

Factor $7 x$ out of $- 42 x$ .

$\frac{(x + 6) (x - 6)}{7 x (x) + 7 x (- 6)}$

Factor $7 x$ out of $7 x (x) + 7 x (- 6)$ .

$\frac{(x + 6) (x - 6)}{7 x (x - 6)}$

Cancel the common factor of $x - 6$ .

Cancel the common factor.

$\frac{(x + 6) (x - 6)}{7 x (x - 6)}$

Rewrite the expression.

$\frac{x + 6}{7 x}$