Algebra Examples

$\frac{5 a + 15}{8} \div \frac{a^{2} - 9}{4 a}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 a + 15}{8} \cdot \frac{4 a}{a^{2} - 9}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $4$ .

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Step 2.1.1

Factor $4$ out of $8$ .

$\frac{5 a + 15}{4 (2)} \cdot \frac{4 a}{a^{2} - 9}$

Step 2.1.2

Factor $4$ out of $4 a$ .

$\frac{5 a + 15}{4 (2)} \cdot \frac{4 (a)}{a^{2} - 9}$

Step 2.1.3

Cancel the common factor.

$\frac{5 a + 15}{4 \cdot 2} \cdot \frac{4 a}{a^{2} - 9}$

Step 2.1.4

Rewrite the expression.

$\frac{5 a + 15}{2} \cdot \frac{a}{a^{2} - 9}$

Step 2.2

Multiply $\frac{5 a + 15}{2}$ by $\frac{a}{a^{2} - 9}$ .

$\frac{(5 a + 15) a}{2 (a^{2} - 9)}$

Step 2.3

Factor $5$ out of $5 a + 15$ .

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Step 2.3.1

Factor $5$ out of $5 a$ .

$\frac{(5 (a) + 15) a}{2 (a^{2} - 9)}$

Step 2.3.2

Factor $5$ out of $15$ .

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

Step 2.3.3

Factor $5$ out of $5 a + 5 \cdot 3$ .

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

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

$\frac{5 (a + 3) a}{2 (a + 3) (a - 3)}$

Step 4

Cancel the common factor of $a + 3$ .

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Step 4.1

Cancel the common factor.

$\frac{5 (a + 3) a}{2 (a + 3) (a - 3)}$

Step 4.2

Rewrite the expression.

$\frac{5 a}{2 (a - 3)}$