Algebra Examples

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

Step 1

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 $b = y$ .

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $x + y$ .

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Step 2.1.1

Cancel the common factor.

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

Step 2.1.2

Rewrite the expression.

$\frac{x - y}{{(x - y)}^{2}}$

Step 2.2

Cancel the common factor of $x - y$ and ${(x - y)}^{2}$ .

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Step 2.2.1

Multiply by $1$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x - y$ out of ${(x - y)}^{2}$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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