Simplify ((m^2-3m)/(8x^2))÷((3m)/(8x))

$\frac{m^{2} - 3 m}{8 x^{2}} \div \frac{3 m}{8 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{m^{2} - 3 m}{8 x^{2}} \cdot \frac{8 x}{3 m}$

Step 2

Cancel the common factor of $8 x$ .

Factor $8 x$ out of $8 x^{2}$ .

$\frac{m^{2} - 3 m}{8 x (x)} \cdot \frac{8 x}{3 m}$

Cancel the common factor.

$\frac{m^{2} - 3 m}{8 x \cdot x} \cdot \frac{8 x}{3 m}$

Rewrite the expression.

$\frac{m^{2} - 3 m}{x} \cdot \frac{1}{3 m}$

Step 3

Multiply $\frac{m^{2} - 3 m}{x}$ by $\frac{1}{3 m}$ .

$\frac{m^{2} - 3 m}{x (3 m)}$

Step 4

Factor $m$ out of $m^{2} - 3 m$ .

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

$\frac{m \cdot m - 3 m}{x \cdot 3 m}$

Factor $m$ out of $- 3 m$ .

$\frac{m \cdot m + m \cdot - 3}{x \cdot 3 m}$

Factor $m$ out of $m \cdot m + m \cdot - 3$ .

$\frac{m (m - 3)}{x \cdot 3 m}$

Step 5

Cancel the common factor of $m$ .

Cancel the common factor.

$\frac{m (m - 3)}{x \cdot 3 m}$

Rewrite the expression.

$\frac{m - 3}{x \cdot 3}$

Step 6

Move $3$ to the left of $x$ .

$\frac{m - 3}{3 x}$