Simplify (x^2-1)/(5xy)*(x^2y)/(1+x)

$\frac{x^{2} - 1}{5 x y} \cdot \frac{x^{2} y}{1 + x}$

Step 1

Simplify the numerator.

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

$\frac{x^{2} - 1^{2}}{5 x y} \cdot \frac{x^{2} y}{1 + x}$

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 $b = 1$ .

$\frac{(x + 1) (x - 1)}{5 x y} \cdot \frac{x^{2} y}{1 + x}$

Step 2

Simplify terms.

Cancel the common factor of $x y$ .

Factor $x y$ out of $5 x y$ .

$\frac{(x + 1) (x - 1)}{x y (5)} \cdot \frac{x^{2} y}{1 + x}$

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

$\frac{(x + 1) (x - 1)}{x y (5)} \cdot \frac{x y (x)}{1 + x}$

Cancel the common factor.

$\frac{(x + 1) (x - 1)}{x y \cdot 5} \cdot \frac{x y x}{1 + x}$

Rewrite the expression.

$\frac{(x + 1) (x - 1)}{5} \cdot \frac{x}{1 + x}$

Multiply $\frac{(x + 1) (x - 1)}{5}$ by $\frac{x}{1 + x}$ .

$\frac{(x + 1) (x - 1) x}{5 (1 + x)}$

Cancel the common factor of $x + 1$ and $1 + x$ .

Reorder terms.

$\frac{(x + 1) (x - 1) x}{5 (x + 1)}$

Cancel the common factor.

$\frac{(x + 1) (x - 1) x}{5 (x + 1)}$

Rewrite the expression.

$\frac{(x - 1) x}{5}$

Reorder factors in $\frac{(x - 1) x}{5}$ .

$\frac{x (x - 1)}{5}$