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

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

Multiply the numerator by the reciprocal of the denominator.

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

Simplify the denominator.

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

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

Combine $- 3$ and $\frac{x - 3}{x - 3}$ .

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

Combine the numerators over the common denominator.

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

Rewrite $\frac{x - 3 (x - 3)}{x - 3}$ in a factored form.

Apply the distributive property.

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

Multiply $- 3$ by $- 3$ .

$\frac{x}{x - 3} \cdot \frac{1}{\frac{x - 3 x + 9}{x - 3}}$

Subtract $3 x$ from $x$ .

$\frac{x}{x - 3} \cdot \frac{1}{\frac{- 2 x + 9}{x - 3}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{x}{x - 3} (1 \frac{x - 3}{- 2 x + 9})$

Multiply $\frac{x - 3}{- 2 x + 9}$ by $1$ .

$\frac{x}{x - 3} \cdot \frac{x - 3}{- 2 x + 9}$

Cancel the common factor of $x - 3$ .

Cancel the common factor.

$\frac{x}{x - 3} \cdot \frac{x - 3}{- 2 x + 9}$

Rewrite the expression.

$x \frac{1}{- 2 x + 9}$

Combine $x$ and $\frac{1}{- 2 x + 9}$ .

$\frac{x}{- 2 x + 9}$

Factor $- 1$ out of $- 2 x$ .

$\frac{x}{- (2 x) + 9}$

Rewrite $9$ as $- 1 (- 9)$ .

$\frac{x}{- (2 x) - 1 (- 9)}$

Factor $- 1$ out of $- (2 x) - 1 (- 9)$ .

$\frac{x}{- (2 x - 9)}$

Rewrite negatives.

Rewrite $- (2 x - 9)$ as $- 1 (2 x - 9)$ .

$\frac{x}{- 1 (2 x - 9)}$

Move the negative in front of the fraction.

$- \frac{x}{2 x - 9}$