Basic Math Examples

$\frac{2 c - 16}{3 c - 5} \div \frac{c - 8}{2 c + 6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 c - 16}{3 c - 5} \cdot \frac{2 c + 6}{c - 8}$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Factor $2$ out of $2 c - 16$ .

Tap for more steps...

Step 2.1.1

Factor $2$ out of $2 c$ .

$\frac{2 (c) - 16}{3 c - 5} \cdot \frac{2 c + 6}{c - 8}$

Step 2.1.2

Factor $2$ out of $- 16$ .

$\frac{2 c + 2 \cdot - 8}{3 c - 5} \cdot \frac{2 c + 6}{c - 8}$

Step 2.1.3

Factor $2$ out of $2 c + 2 \cdot - 8$ .

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

Step 2.2

Cancel the common factor of $c - 8$ .

Tap for more steps...

Step 2.2.1

Factor $c - 8$ out of $2 (c - 8)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\frac{2}{3 c - 5} (2 c + 6)$

Step 2.3

Multiply $\frac{2}{3 c - 5}$ by $2 c + 6$ .

$\frac{2 (2 c + 6)}{3 c - 5}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Factor $2$ out of $2 c + 6$ .

Tap for more steps...

Step 3.1.1

Factor $2$ out of $2 c$ .

$\frac{2 (2 (c) + 6)}{3 c - 5}$

Step 3.1.2

Factor $2$ out of $6$ .

$\frac{2 (2 c + 2 \cdot 3)}{3 c - 5}$

Step 3.1.3

Factor $2$ out of $2 c + 2 \cdot 3$ .

$\frac{2 (2 (c + 3))}{3 c - 5}$

$\frac{2 \cdot 2 (c + 3)}{3 c - 5}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{4 (c + 3)}{3 c - 5}$