Simplify (x-7)/(x^2-49)

$\frac{x - 7}{x^{2} - 49}$

Step 1

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

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

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 $b = 7$ .

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

Step 2

Cancel the common factor of $x - 7$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x + 7}$