Basic Math Examples

$\frac{3}{a^{2} - 9} \div \frac{5}{a + 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{3}{a^{2} - 3^{2}} \cdot \frac{a + 3}{5}$

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 $a = a$ and $b = 3$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $a + 3$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

$\frac{3}{a - 3} \cdot \frac{1}{5}$

Step 3.2

Multiply $\frac{3}{a - 3}$ by $\frac{1}{5}$ .

$\frac{3}{(a - 3) \cdot 5}$

Step 3.3

Move $5$ to the left of $a - 3$ .

$\frac{3}{5 (a - 3)}$