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

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

Simplify the denominator.

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

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

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 $b = 1$ .

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

Simplify terms.

Cancel the common factor of $x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{x}$ by $\frac{1}{x - 1}$ .

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