Basic Math Examples

$\frac{a^{2 - 9}}{8 a + 24} \div \frac{3 - a}{8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2 - 9}}{8 a + 24} \cdot \frac{8}{3 - a}$

Step 2

Move $a^{2 - 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{(8 a + 24) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Step 3

Simplify the denominator.

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Step 3.1

Factor $8$ out of $8 a + 24$ .

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Step 3.1.1

Factor $8$ out of $8 a$ .

$\frac{1}{(8 (a) + 24) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Step 3.1.2

Factor $8$ out of $24$ .

$\frac{1}{(8 a + 8 \cdot 3) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Step 3.1.3

Factor $8$ out of $8 a + 8 \cdot 3$ .

$\frac{1}{8 (a + 3) a^{- (2 - 9)}} \cdot \frac{8}{3 - a}$

Step 3.2

Subtract $9$ from $2$ .

$\frac{1}{8 (a + 3) a^{- - 7}} \cdot \frac{8}{3 - a}$

Step 3.3

Multiply $- 1$ by $- 7$ .

$\frac{1}{8 (a + 3) a^{7}} \cdot \frac{8}{3 - a}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $8$ .

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Step 4.1.1

Factor $8$ out of $8 (a + 3) a^{7}$ .

$\frac{1}{8 ((a + 3) a^{7})} \cdot \frac{8}{3 - a}$

Step 4.1.2

Cancel the common factor.

$\frac{1}{8 ((a + 3) a^{7})} \cdot \frac{8}{3 - a}$

Step 4.1.3

Rewrite the expression.

$\frac{1}{(a + 3) a^{7}} \cdot \frac{1}{3 - a}$

Step 4.2

Multiply $\frac{1}{(a + 3) a^{7}}$ by $\frac{1}{3 - a}$ .

$\frac{1}{(a + 3) a^{7} (3 - a)}$

Step 4.3

Reorder factors in $\frac{1}{(a + 3) a^{7} (3 - a)}$ .

$\frac{1}{a^{7} (a + 3) (3 - a)}$