Simplify (x^2-16)/(x^4-x^3)

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

Step 1

Simplify the numerator.

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

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

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 $b = 4$ .

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

Step 2

Factor $x^{3}$ out of $x^{4} - x^{3}$ .

Factor $x^{3}$ out of $x^{4}$ .

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

Factor $x^{3}$ out of $- x^{3}$ .

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

Factor $x^{3}$ out of $x^{3} x + x^{3} \cdot - 1$ .

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