Simplify (x^2-2x)/2*(6x^2)/(x-2)

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

Step 1

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

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

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

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

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

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

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

Step 2

Cancel the common factor of $x - 2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{2} \cdot (6 x^{2})$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $6 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x \cdot (3 x^{2})$

Step 4

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

$3 (x^{1} x^{2})$

Step 5

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

$3 x^{1 + 2}$

Step 6

Add $1$ and $2$ .

$3 x^{3}$