Finite Math Examples

$\frac{\frac{8 x}{x^{2} - 49}}{\frac{4 x - 32}{7 x + 99}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 x}{x^{2} - 49} \cdot \frac{7 x + 99}{4 x - 32}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $49$ as $7^{2}$ .

$\frac{8 x}{x^{2} - 7^{2}} \cdot \frac{7 x + 99}{4 x - 32}$

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 $a = x$ and $b = 7$ .

$\frac{8 x}{(x + 7) (x - 7)} \cdot \frac{7 x + 99}{4 x - 32}$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Factor $4$ out of $4 x - 32$ .

Tap for more steps...

Step 3.1.1

Factor $4$ out of $4 x$ .

$\frac{8 x}{(x + 7) (x - 7)} \cdot \frac{7 x + 99}{4 (x) - 32}$

Step 3.1.2

Factor $4$ out of $- 32$ .

$\frac{8 x}{(x + 7) (x - 7)} \cdot \frac{7 x + 99}{4 x + 4 \cdot - 8}$

Step 3.1.3

Factor $4$ out of $4 x + 4 \cdot - 8$ .

$\frac{8 x}{(x + 7) (x - 7)} \cdot \frac{7 x + 99}{4 (x - 8)}$

Step 3.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.1

Factor $4$ out of $8 x$ .

$\frac{4 (2 x)}{(x + 7) (x - 7)} \cdot \frac{7 x + 99}{4 (x - 8)}$

Step 3.2.2

Cancel the common factor.

$\frac{4 (2 x)}{(x + 7) (x - 7)} \cdot \frac{7 x + 99}{4 (x - 8)}$

Step 3.2.3

Rewrite the expression.

$\frac{2 x}{(x + 7) (x - 7)} \cdot \frac{7 x + 99}{x - 8}$

Step 3.3

Multiply $\frac{2 x}{(x + 7) (x - 7)}$ by $\frac{7 x + 99}{x - 8}$ .

$\frac{2 x (7 x + 99)}{(x + 7) (x - 7) (x - 8)}$