Pre-Algebra Examples

$\frac{\frac{x - 3}{x^{2} - 16}}{1 + \frac{1}{x - 4}}$

Step 1

Rewrite $16$ as $4^{2}$ .

$\frac{\frac{x - 3}{x^{2} - 4^{2}}}{1 + \frac{1}{x - 4}}$

Step 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 $b = 4$ .

$\frac{\frac{x - 3}{(x + 4) (x - 4)}}{1 + \frac{1}{x - 4}}$

Step 3

Write $1$ as a fraction with a common denominator.

$\frac{\frac{x - 3}{(x + 4) (x - 4)}}{\frac{x - 4}{x - 4} + \frac{1}{x - 4}}$

Step 4

Combine the numerators over the common denominator.

$\frac{\frac{x - 3}{(x + 4) (x - 4)}}{\frac{x - 4 + 1}{x - 4}}$

Step 5

Add $- 4$ and $1$ .

$\frac{\frac{x - 3}{(x + 4) (x - 4)}}{\frac{x - 3}{x - 4}}$