Basic Math Examples

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

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

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

Step 2

Move

a^{2 - 9}

$a^{2 - 9}$ to the denominator using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

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

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

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Factor

8

$8$ out of

8 a + 24

$8 a + 24$ .

Tap for more steps...

Step 3.1.1

Factor

8

$8$ out of

8 a

$8 a$ .

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

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

Step 3.1.2

Factor

8

$8$ out of

24

$24$ .

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

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

Step 3.1.3

Factor

8

$8$ out of

8 a + 8 \cdot 3

$8 a + 8 \cdot 3$ .

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

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

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

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

Step 3.2

Subtract

9

$9$ from

2

$2$ .

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

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

Step 3.3

Multiply

- 1

$- 1$ by

- 7

$- 7$ .

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

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

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

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

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Cancel the common factor of

8

$8$ .

Tap for more steps...

Step 4.1.1

Factor

8

$8$ out of

8 (a + 3) a^{7}

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

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

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

Step 4.1.2

Cancel the common factor.

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

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

Step 4.1.3

Rewrite the expression.

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

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

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

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

Step 4.2

Multiply

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

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

\frac{1}{3 - a}

$\frac{1}{3 - a}$ .

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

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

Step 4.3

Reorder factors in

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

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

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

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

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

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