Pre-Algebra Examples

$\frac{\frac{2 x + 16}{x - 6}}{\frac{6 x + 48}{5 x - 30}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 x + 16}{x - 6} \cdot \frac{5 x - 30}{6 x + 48}$

Step 2

Factor $2$ out of $2 x + 16$ .

Tap for more steps...

Step 2.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 16}{x - 6} \cdot \frac{5 x - 30}{6 x + 48}$

Step 2.2

Factor $2$ out of $16$ .

$\frac{2 x + 2 \cdot 8}{x - 6} \cdot \frac{5 x - 30}{6 x + 48}$

Step 2.3

Factor $2$ out of $2 x + 2 \cdot 8$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 x - 30}{6 x + 48}$

Step 3

Factor $5$ out of $5 x - 30$ .

Tap for more steps...

Step 3.1

Factor $5$ out of $5 x$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 (x) - 30}{6 x + 48}$

Step 3.2

Factor $5$ out of $- 30$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 x + 5 \cdot - 6}{6 x + 48}$

Step 3.3

Factor $5$ out of $5 x + 5 \cdot - 6$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 (x - 6)}{6 x + 48}$

Step 4

Factor $6$ out of $6 x + 48$ .

Tap for more steps...

Step 4.1

Factor $6$ out of $6 x$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 (x - 6)}{6 (x) + 48}$

Step 4.2

Factor $6$ out of $48$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 (x - 6)}{6 x + 6 \cdot 8}$

Step 4.3

Factor $6$ out of $6 x + 6 \cdot 8$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 (x - 6)}{6 (x + 8)}$

Step 5

Cancel the common factor of $2 (x + 8)$ .

Tap for more steps...

Step 5.1

Factor $2 (x + 8)$ out of $6 (x + 8)$ .

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 (x - 6)}{2 (x + 8) (3)}$

Step 5.2

Cancel the common factor.

$\frac{2 (x + 8)}{x - 6} \cdot \frac{5 (x - 6)}{2 (x + 8) \cdot 3}$

Step 5.3

Rewrite the expression.

$\frac{1}{x - 6} \cdot \frac{5 (x - 6)}{3}$

Step 6

Cancel the common factor of $x - 6$ .

Tap for more steps...

Step 6.1

Factor $x - 6$ out of $5 (x - 6)$ .

$\frac{1}{x - 6} \cdot \frac{(x - 6) \cdot 5}{3}$

Step 6.2

Cancel the common factor.

$\frac{1}{x - 6} \cdot \frac{(x - 6) \cdot 5}{3}$

Step 6.3

Rewrite the expression.

$\frac{5}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$