Algebra Examples

$\frac{x}{x - 5} \div \frac{x y}{x^{2} - 25}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x}{x - 5} \cdot \frac{x^{2} - 25}{x y}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $x$ .

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Step 2.1.1

Factor $x$ out of $x y$ .

$\frac{x}{x - 5} \cdot \frac{x^{2} - 25}{x (y)}$

Step 2.1.2

Cancel the common factor.

$\frac{x}{x - 5} \cdot \frac{x^{2} - 25}{x y}$

Step 2.1.3

Rewrite the expression.

$\frac{1}{x - 5} \cdot \frac{x^{2} - 25}{y}$

Step 2.2

Multiply $\frac{1}{x - 5}$ by $\frac{x^{2} - 25}{y}$ .

$\frac{x^{2} - 25}{(x - 5) y}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $25$ as $5^{2}$ .

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

Step 3.2

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 $b = 5$ .

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

Step 4

Cancel the common factor of $x - 5$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{x + 5}{y}$