Pre-Algebra Examples

$(2 a + 6) \div \frac{a^{2} - 9}{2 a}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(2 a + 6) \frac{2 a}{a^{2} - 9}$

Step 2

Simplify the denominator.

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Step 2.1

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

$(2 a + 6) \frac{2 a}{a^{2} - 3^{2}}$

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 $b = 3$ .

$(2 a + 6) \frac{2 a}{(a + 3) (a - 3)}$

Step 3

Multiply $2 a + 6$ by $\frac{2 a}{(a + 3) (a - 3)}$ .

$\frac{(2 a + 6) (2 a)}{(a + 3) (a - 3)}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $2$ out of $2 a + 6$ .

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Step 4.1.1

Factor $2$ out of $2 a$ .

$\frac{(2 (a) + 6) \cdot 2 a}{(a + 3) (a - 3)}$

Step 4.1.2

Factor $2$ out of $6$ .

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

Step 4.1.3

Factor $2$ out of $2 a + 2 \cdot 3$ .

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

Step 4.2

Multiply $2$ by $2$ .

$\frac{4 (a + 3) a}{(a + 3) (a - 3)}$

Step 5

Cancel the common factor of $a + 3$ .

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Step 5.1

Cancel the common factor.

$\frac{4 (a + 3) a}{(a + 3) (a - 3)}$

Step 5.2

Rewrite the expression.

$\frac{4 a}{a - 3}$