Algebra Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Raise $x - y$ to the power of $1$ .

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

Step 1.2

Raise $x - y$ to the power of $1$ .

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

Step 1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.4

Add $1$ and $1$ .

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x - y$ .

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Step 2.1.1

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

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

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

Step 2.2

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

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