Basic Math Examples

$\frac{11 y}{y^{2} - 16} \cdot \frac{y + 4}{5 y}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{11 y}{y^{2} - 4^{2}} \cdot \frac{y + 4}{5 y}$

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 $b = 4$ .

$\frac{11 y}{(y + 4) (y - 4)} \cdot \frac{y + 4}{5 y}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $y$ .

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Step 2.1.1

Factor $y$ out of $11 y$ .

$\frac{y \cdot 11}{(y + 4) (y - 4)} \cdot \frac{y + 4}{5 y}$

Step 2.1.2

Factor $y$ out of $5 y$ .

$\frac{y \cdot 11}{(y + 4) (y - 4)} \cdot \frac{y + 4}{y \cdot 5}$

Step 2.1.3

Cancel the common factor.

$\frac{y \cdot 11}{(y + 4) (y - 4)} \cdot \frac{y + 4}{y \cdot 5}$

Step 2.1.4

Rewrite the expression.

$\frac{11}{(y + 4) (y - 4)} \cdot \frac{y + 4}{5}$

Step 2.2

Cancel the common factor of $y + 4$ .

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Step 2.2.1

Cancel the common factor.

$\frac{11}{(y + 4) (y - 4)} \cdot \frac{y + 4}{5}$

Step 2.2.2

Rewrite the expression.

$\frac{11}{y - 4} \cdot \frac{1}{5}$

Step 2.3

Multiply $\frac{11}{y - 4}$ by $\frac{1}{5}$ .

$\frac{11}{(y - 4) \cdot 5}$

Step 2.4

Move $5$ to the left of $y - 4$ .

$\frac{11}{5 (y - 4)}$