Simplify (x/3-1)/(x-3)

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

Step 1

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

Multiply $\frac{\frac{x}{3} - 1}{x - 3}$ by $\frac{3}{3}$ .

$\frac{3}{3} \cdot \frac{\frac{x}{3} - 1}{x - 3}$

Combine.

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

Step 2

Apply the distributive property.

$\frac{3 \frac{x}{3} + 3 \cdot - 1}{3 x + 3 \cdot - 3}$

Step 3

Simplify terms.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \frac{x}{3} + 3 \cdot - 1}{3 x + 3 \cdot - 3}$

Rewrite the expression.

$\frac{x + 3 \cdot - 1}{3 x + 3 \cdot - 3}$

Multiply $3$ by $- 1$ .

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

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $3 \cdot - 3$ .

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

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

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

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$