Basic Math Examples

$\frac{y^{2} - 36}{2 y + 16} \cdot \frac{y + 8}{y - 6}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{y^{2} - 6^{2}}{2 y + 16} \cdot \frac{y + 8}{y - 6}$

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 $a = y$ and $b = 6$ .

$\frac{(y + 6) (y - 6)}{2 y + 16} \cdot \frac{y + 8}{y - 6}$

Step 2

Simplify terms.

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Step 2.1

Factor $2$ out of $2 y + 16$ .

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Step 2.1.1

Factor $2$ out of $2 y$ .

$\frac{(y + 6) (y - 6)}{2 (y) + 16} \cdot \frac{y + 8}{y - 6}$

Step 2.1.2

Factor $2$ out of $16$ .

$\frac{(y + 6) (y - 6)}{2 y + 2 \cdot 8} \cdot \frac{y + 8}{y - 6}$

Step 2.1.3

Factor $2$ out of $2 y + 2 \cdot 8$ .

$\frac{(y + 6) (y - 6)}{2 (y + 8)} \cdot \frac{y + 8}{y - 6}$

Step 2.2

Cancel the common factor of $y - 6$ .

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Step 2.2.1

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

$\frac{(y - 6) (y + 6)}{2 (y + 8)} \cdot \frac{y + 8}{y - 6}$

Step 2.2.2

Cancel the common factor.

$\frac{(y - 6) (y + 6)}{2 (y + 8)} \cdot \frac{y + 8}{y - 6}$

Step 2.2.3

Rewrite the expression.

$\frac{y + 6}{2 (y + 8)} \cdot (y + 8)$

Step 2.3

Cancel the common factor of $y + 8$ .

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Step 2.3.1

Factor $y + 8$ out of $2 (y + 8)$ .

$\frac{y + 6}{(y + 8) \cdot 2} \cdot (y + 8)$

Step 2.3.2

Cancel the common factor.

$\frac{y + 6}{(y + 8) \cdot 2} \cdot (y + 8)$

Step 2.3.3

Rewrite the expression.

$\frac{y + 6}{2}$