Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

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

Step 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 $b = 1$ .

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Cancel the common factor of $x y$ .

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

Cancel the common factor.

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

Step 2.1.4

Rewrite the expression.

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

Step 2.2

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

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

Step 2.3

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

Tap for more steps...

Step 2.3.1

Reorder terms.

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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

Step 2.4

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

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