Simplify ((x^2)/(x-3))/(x/((x-3)^2))

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x - 3$ .

Factor $x - 3$ out of ${(x - 3)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x (x - 3)$

Step 4

Apply the distributive property.

$x \cdot x + x \cdot - 3$

Step 5

Simplify the expression.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3$

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

$x^{2} - 3 x$