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

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

Step 1

Simplify the numerator.

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

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

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

Step 2

Cancel the common factor of $1 - x$ .

Cancel the common factor.

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

Rewrite the expression.

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