Simplify (x^2-1)/(x^3-x^2)

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

Step 1

Simplify the numerator.

Rewrite $1$ as $1^{2}$ .

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

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 $b = 1$ .

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

Step 2

Simplify terms.

Factor $x^{2}$ out of $x^{3} - x^{2}$ .

Factor $x^{2}$ out of $x^{3}$ .

$\frac{(x + 1) (x - 1)}{x^{2} x - x^{2}}$

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

$\frac{(x + 1) (x - 1)}{x^{2} x + x^{2} \cdot - 1}$

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot - 1$ .

$\frac{(x + 1) (x - 1)}{x^{2} (x - 1)}$

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{(x + 1) (x - 1)}{x^{2} (x - 1)}$

Rewrite the expression.

$\frac{x + 1}{x^{2}}$