Divide ((x^2-2x)/6)÷((3x-6)/x)

$\frac{x^{2} - 2 x}{6} \div \frac{3 x - 6}{x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 2 x}{6} \cdot \frac{x}{3 x - 6}$

Step 2

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

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

$\frac{x \cdot x - 2 x}{6} \cdot \frac{x}{3 x - 6}$

Factor $x$ out of $- 2 x$ .

$\frac{x \cdot x + x \cdot - 2}{6} \cdot \frac{x}{3 x - 6}$

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

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

Step 3

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 6$ .

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

Factor $3$ out of $3 x + 3 \cdot - 2$ .

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

Step 4

Cancel the common factor of $x - 2$ .

Factor $x - 2$ out of $x (x - 2)$ .

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

Factor $x - 2$ out of $3 (x - 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{6} \cdot \frac{x}{3}$

Step 5

Multiply $\frac{x}{6}$ by $\frac{x}{3}$ .

$\frac{x \cdot x}{6 \cdot 3}$

Step 6

Raise $x$ to the power of $1$ .

$\frac{x^{1} x}{6 \cdot 3}$

Step 7

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{1}}{6 \cdot 3}$

Step 8

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{1 + 1}}{6 \cdot 3}$

Step 9

Add $1$ and $1$ .

$\frac{x^{2}}{6 \cdot 3}$

Step 10

Multiply $6$ by $3$ .

$\frac{x^{2}}{18}$

Divide ((x^2-2x)/6)÷((3x-6)/x)

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