Basic Math Examples

$\frac{{(y + 3)}^{2}}{y^{2} - 9} \div \frac{3 y + 9}{y + 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{{(y + 3)}^{2}}{y^{2} - 9} \cdot \frac{y + 3}{3 y + 9}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{{(y + 3)}^{2}}{y^{2} - 3^{2}} \cdot \frac{y + 3}{3 y + 9}$

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 $b = 3$ .

$\frac{{(y + 3)}^{2}}{(y + 3) (y - 3)} \cdot \frac{y + 3}{3 y + 9}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $y + 3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{{(y + 3)}^{2}}{(y + 3) (y - 3)} \cdot \frac{y + 3}{3 y + 9}$

Step 3.1.2

Rewrite the expression.

$\frac{{(y + 3)}^{2}}{y - 3} \cdot \frac{1}{3 y + 9}$

Step 3.2

Multiply $\frac{{(y + 3)}^{2}}{y - 3}$ by $\frac{1}{3 y + 9}$ .

$\frac{{(y + 3)}^{2}}{(y - 3) (3 y + 9)}$

Step 4

Factor $3$ out of $3 y + 9$ .

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Step 4.1

Factor $3$ out of $3 y$ .

$\frac{{(y + 3)}^{2}}{(y - 3) (3 (y) + 9)}$

Step 4.2

Factor $3$ out of $9$ .

$\frac{{(y + 3)}^{2}}{(y - 3) (3 y + 3 \cdot 3)}$

Step 4.3

Factor $3$ out of $3 y + 3 \cdot 3$ .

$\frac{{(y + 3)}^{2}}{(y - 3) (3 (y + 3))}$

$\frac{{(y + 3)}^{2}}{(y - 3) \cdot 3 (y + 3)}$

Step 5

Cancel the common factor of ${(y + 3)}^{2}$ and $y + 3$ .

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Step 5.1

Factor $y + 3$ out of ${(y + 3)}^{2}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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