Basic Math Examples

\frac{y^{2}}{y + 3} - \frac{9}{y + 3}

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

Step 1

Combine the numerators over the common denominator.

\frac{y^{2} - 9}{y + 3}

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

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

\frac{y^{2} - 3^{2}}{y + 3}

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

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = y

$a = y$ and

b = 3

$b = 3$ .

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

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

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

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

Step 3

Cancel the common factor of

y + 3

$y + 3$ .

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Step 3.1

Cancel the common factor.

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

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

Step 3.2

Divide

y - 3

$y - 3$ by

1

$1$ .

y - 3

$y - 3$

y - 3

$y - 3$