Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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Step 2.1

Factor $3$ out of $3 y$ .

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

Step 2.2

Factor $3$ out of $- 9$ .

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

Step 2.3

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

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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 $b = 3$ .

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

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $y + 3$ .

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Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $y - 3$ .

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 4.3

Multiply $y + 3$ by $\frac{3}{y - 3}$ .

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

Step 4.4

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

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