Simplify (x^2-1)/(3x)*(6x)/(2x-2)

$\frac{x^{2} - 1}{3 x} \cdot \frac{6 x}{2 x - 2}$

Simplify the numerator.

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

$\frac{x^{2} - 1^{2}}{3 x} \cdot \frac{6 x}{2 x - 2}$

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 $b = 1$ .

$\frac{(x + 1) (x - 1)}{3 x} \cdot \frac{6 x}{2 x - 2}$

Simplify terms.

Factor $2$ out of $2 x - 2$ .

Factor $2$ out of $2 x$ .

$\frac{(x + 1) (x - 1)}{3 x} \cdot \frac{6 x}{2 (x) - 2}$

Factor $2$ out of $- 2$ .

$\frac{(x + 1) (x - 1)}{3 x} \cdot \frac{6 x}{2 (x) + 2 (- 1)}$

Factor $2$ out of $2 (x) + 2 (- 1)$ .

$\frac{(x + 1) (x - 1)}{3 x} \cdot \frac{6 x}{2 (x - 1)}$

Cancel the common factor of $x - 1$ .

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

$\frac{(x - 1) (x + 1)}{3 x} \cdot \frac{6 x}{2 (x - 1)}$

Factor $x - 1$ out of $2 (x - 1)$ .

$\frac{(x - 1) (x + 1)}{3 x} \cdot \frac{6 x}{(x - 1) \cdot 2}$

Cancel the common factor.

$\frac{(x - 1) (x + 1)}{3 x} \cdot \frac{6 x}{(x - 1) \cdot 2}$

Rewrite the expression.

$\frac{x + 1}{3 x} \cdot \frac{6 x}{2}$

Cancel the common factor of $3 x$ .

Factor $3 x$ out of $6 x$ .

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

Cancel the common factor.

$\frac{x + 1}{3 x} \cdot \frac{3 x \cdot 2}{2}$

Rewrite the expression.

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

Simplify the expression.

Divide $2$ by $2$ .

$(x + 1) \cdot 1$

Multiply $x + 1$ by $1$ .

$x + 1$