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

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

Step 1

Multiply the numerator and denominator of the complex fraction by $3$ .

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

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

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

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

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

$\frac{x \cdot x + x (3 \cdot (- 1))}{3 x^{2} + 3 (- x)}$

Factor $x$ out of $x \cdot x + x (3 \cdot (- 1))$ .

$\frac{x (x + 3 \cdot (- 1))}{3 x^{2} + 3 (- x)}$

Multiply $3$ by $- 1$ .

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

Step 5

Simplify terms.

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

Factor $3 x$ out of $3 x^{2}$ .

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

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

$\frac{x (x - 3)}{3 x (x) + 3 x (- 1)}$

Factor $3 x$ out of $3 x (x) + 3 x (- 1)$ .

$\frac{x (x - 3)}{3 x (x - 1)}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (x - 3)}{3 x (x - 1)}$

Rewrite the expression.

$\frac{x - 3}{3 (x - 1)}$