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

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

Step 1

Simplify the denominator.

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

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

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

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

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 1$ .

Factor $x - 1$ out of $(x + 1) (x - 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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