Simplify ((18x^2)/(x-1))/(x/(2x-2))

$\frac{\frac{18 x^{2}}{x - 1}}{\frac{x}{2 x - 2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{18 x^{2}}{x - 1} \cdot \frac{2 x - 2}{x}$

Step 2

Simplify terms.

Cancel the common factor of $x$ .

Factor $x$ out of $18 x^{2}$ .

$\frac{x (18 x)}{x - 1} \cdot \frac{2 x - 2}{x}$

Cancel the common factor.

$\frac{x (18 x)}{x - 1} \cdot \frac{2 x - 2}{x}$

Rewrite the expression.

$\frac{18 x}{x - 1} (2 x - 2)$

Multiply $\frac{18 x}{x - 1}$ by $2 x - 2$ .

$\frac{18 x (2 x - 2)}{x - 1}$

Step 3

Simplify the numerator.

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

Factor $2$ out of $2 x$ .

$\frac{18 x (2 (x) - 2)}{x - 1}$

Factor $2$ out of $- 2$ .

$\frac{18 x (2 (x) + 2 (- 1))}{x - 1}$

Factor $2$ out of $2 (x) + 2 (- 1)$ .

$\frac{18 x (2 (x - 1))}{x - 1}$

$\frac{18 x \cdot 2 (x - 1)}{x - 1}$

Multiply $2$ by $18$ .

$\frac{36 x (x - 1)}{x - 1}$

Step 4

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{36 x (x - 1)}{x - 1}$

Divide $36 x$ by $1$ .

$36 x$