Simplify ((2b^2-12b)/(b+5))÷((b-6)/(b+5))

$\frac{2 b^{2} - 12 b}{b + 5} \div \frac{b - 6}{b + 5}$

To divide by a fraction, multiply by its reciprocal.

$\frac{2 b^{2} - 12 b}{b + 5} \cdot \frac{b + 5}{b - 6}$

Cancel the common factor of $b + 5$ .

Cancel the common factor.

$\frac{2 b^{2} - 12 b}{b + 5} \cdot \frac{b + 5}{b - 6}$

Rewrite the expression.

$(2 b^{2} - 12 b) \frac{1}{b - 6}$

Multiply $2 b^{2} - 12 b$ by $\frac{1}{b - 6}$ .

$\frac{2 b^{2} - 12 b}{b - 6}$

Factor $2 b$ out of $2 b^{2} - 12 b$ .

Factor $2 b$ out of $2 b^{2}$ .

$\frac{2 b (b) - 12 b}{b - 6}$

Factor $2 b$ out of $- 12 b$ .

$\frac{2 b (b) + 2 b (- 6)}{b - 6}$

Factor $2 b$ out of $2 b (b) + 2 b (- 6)$ .

$\frac{2 b (b - 6)}{b - 6}$

Cancel the common factor of $b - 6$ .

Cancel the common factor.

$\frac{2 b (b - 6)}{b - 6}$

Divide $2 b$ by $1$ .

$2 b$