Basic Math Examples

$\frac{y^{2} - 36}{y} \div \frac{y - 6}{y + 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{y^{2} - 36}{y} \cdot \frac{y + 5}{y - 6}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $36$ as $6^{2}$ .

$\frac{y^{2} - 6^{2}}{y} \cdot \frac{y + 5}{y - 6}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 6$ .

$\frac{(y + 6) (y - 6)}{y} \cdot \frac{y + 5}{y - 6}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $y - 6$ .

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Step 3.1.1

Factor $y - 6$ out of $(y + 6) (y - 6)$ .

$\frac{(y - 6) (y + 6)}{y} \cdot \frac{y + 5}{y - 6}$

Step 3.1.2

Cancel the common factor.

$\frac{(y - 6) (y + 6)}{y} \cdot \frac{y + 5}{y - 6}$

Step 3.1.3

Rewrite the expression.

$\frac{y + 6}{y} (y + 5)$

Step 3.2

Multiply $\frac{y + 6}{y}$ by $y + 5$ .

$\frac{(y + 6) (y + 5)}{y}$