Basic Math Examples

$\frac{s^{2} - 16}{9 s + 36} \div \frac{3 s^{2} - 24 s + 48}{27 s + 108}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{s^{2} - 16}{9 s + 36} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{s^{2} - 4^{2}}{9 s + 36} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

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 $a = s$ and $b = 4$ .

$\frac{(s + 4) (s - 4)}{9 s + 36} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Factor $9$ out of $9 s + 36$ .

Tap for more steps...

Step 3.1.1

Factor $9$ out of $9 s$ .

$\frac{(s + 4) (s - 4)}{9 (s) + 36} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

Step 3.1.2

Factor $9$ out of $36$ .

$\frac{(s + 4) (s - 4)}{9 s + 9 \cdot 4} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

Step 3.1.3

Factor $9$ out of $9 s + 9 \cdot 4$ .

$\frac{(s + 4) (s - 4)}{9 (s + 4)} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

Step 3.2

Cancel the common factor of $s + 4$ .

Tap for more steps...

Step 3.2.1

Cancel the common factor.

$\frac{(s + 4) (s - 4)}{9 (s + 4)} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

Step 3.2.2

Rewrite the expression.

$\frac{s - 4}{9} \cdot \frac{27 s + 108}{3 s^{2} - 24 s + 48}$

Step 3.3

Cancel the common factor of $27 s + 108$ and $3 s^{2} - 24 s + 48$ .

Tap for more steps...

Step 3.3.1

Factor $3$ out of $27 s$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s) + 108}{3 s^{2} - 24 s + 48}$

Step 3.3.2

Factor $3$ out of $108$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s) + 3 \cdot 36}{3 s^{2} - 24 s + 48}$

Step 3.3.3

Factor $3$ out of $3 (9 s) + 3 (36)$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s + 36)}{3 s^{2} - 24 s + 48}$

Step 3.3.4

Cancel the common factors.

Tap for more steps...

Step 3.3.4.1

Factor $3$ out of $3 s^{2}$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s + 36)}{3 (s^{2}) - 24 s + 48}$

Step 3.3.4.2

Factor $3$ out of $- 24 s$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s + 36)}{3 (s^{2}) + 3 (- 8 s) + 48}$

Step 3.3.4.3

Factor $3$ out of $3 (s^{2}) + 3 (- 8 s)$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s + 36)}{3 (s^{2} - 8 s) + 48}$

Step 3.3.4.4

Factor $3$ out of $48$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s + 36)}{3 (s^{2} - 8 s) + 3 \cdot 16}$

Step 3.3.4.5

Factor $3$ out of $3 (s^{2} - 8 s) + 3 \cdot 16$ .

$\frac{s - 4}{9} \cdot \frac{3 (9 s + 36)}{3 (s^{2} - 8 s + 16)}$

Step 3.3.4.6

Cancel the common factor.

$\frac{s - 4}{9} \cdot \frac{3 (9 s + 36)}{3 (s^{2} - 8 s + 16)}$

Step 3.3.4.7

Rewrite the expression.

$\frac{s - 4}{9} \cdot \frac{9 s + 36}{s^{2} - 8 s + 16}$

Step 3.4

Factor $9$ out of $9 s + 36$ .

Tap for more steps...

Step 3.4.1

Factor $9$ out of $9 s$ .

$\frac{s - 4}{9} \cdot \frac{9 (s) + 36}{s^{2} - 8 s + 16}$

Step 3.4.2

Factor $9$ out of $36$ .

$\frac{s - 4}{9} \cdot \frac{9 s + 9 \cdot 4}{s^{2} - 8 s + 16}$

Step 3.4.3

Factor $9$ out of $9 s + 9 \cdot 4$ .

$\frac{s - 4}{9} \cdot \frac{9 (s + 4)}{s^{2} - 8 s + 16}$

Step 4

Factor using the perfect square rule.

Tap for more steps...

Step 4.1

Rewrite $16$ as $4^{2}$ .

$\frac{s - 4}{9} \cdot \frac{9 (s + 4)}{s^{2} - 8 s + 4^{2}}$

Step 4.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 s = 2 \cdot s \cdot 4$

Step 4.3

Rewrite the polynomial.

$\frac{s - 4}{9} \cdot \frac{9 (s + 4)}{s^{2} - 2 \cdot s \cdot 4 + 4^{2}}$

Step 4.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = s$ and $b = 4$ .

$\frac{s - 4}{9} \cdot \frac{9 (s + 4)}{{(s - 4)}^{2}}$

Step 5

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 5.1

Cancel the common factor of $s - 4$ .

Tap for more steps...

Step 5.1.1

Factor $s - 4$ out of ${(s - 4)}^{2}$ .

$\frac{s - 4}{9} \cdot \frac{9 (s + 4)}{(s - 4) (s - 4)}$

Step 5.1.2

Cancel the common factor.

$\frac{s - 4}{9} \cdot \frac{9 (s + 4)}{(s - 4) (s - 4)}$

Step 5.1.3

Rewrite the expression.

$\frac{1}{9} \cdot \frac{9 (s + 4)}{s - 4}$

Step 5.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 5.2.1

Cancel the common factor.

$\frac{1}{9} \cdot \frac{9 (s + 4)}{s - 4}$

Step 5.2.2

Rewrite the expression.

$\frac{s + 4}{s - 4}$