Basic Math Examples

$\frac{y^{2} - 9}{5 y} \cdot \frac{3 y}{y - 3}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{y^{2} - 3^{2}}{5 y} \cdot \frac{3 y}{y - 3}$

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 $b = 3$ .

$\frac{(y + 3) (y - 3)}{5 y} \cdot \frac{3 y}{y - 3}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $y - 3$ .

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Step 2.1.1

Factor $y - 3$ out of $(y + 3) (y - 3)$ .

$\frac{(y - 3) (y + 3)}{5 y} \cdot \frac{3 y}{y - 3}$

Step 2.1.2

Cancel the common factor.

$\frac{(y - 3) (y + 3)}{5 y} \cdot \frac{3 y}{y - 3}$

Step 2.1.3

Rewrite the expression.

$\frac{y + 3}{5 y} \cdot (3 y)$

Step 2.2

Cancel the common factor of $y$ .

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Step 2.2.1

Factor $y$ out of $5 y$ .

$\frac{y + 3}{y \cdot 5} \cdot (3 y)$

Step 2.2.2

Factor $y$ out of $3 y$ .

$\frac{y + 3}{y \cdot 5} \cdot (y \cdot 3)$

Step 2.2.3

Cancel the common factor.

$\frac{y + 3}{y \cdot 5} \cdot (y \cdot 3)$

Step 2.2.4

Rewrite the expression.

$\frac{y + 3}{5} \cdot 3$

Step 2.3

Combine $\frac{y + 3}{5}$ and $3$ .

$\frac{(y + 3) \cdot 3}{5}$

Step 2.4

Move $3$ to the left of $y + 3$ .

$\frac{3 (y + 3)}{5}$