Simplify (2/(x-3))/(-1/(x-3)+3/x)

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

Multiply the numerator by the reciprocal of the denominator.

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

Simplify the denominator.

To write $\frac{- 1}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

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

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

Write each expression with a common denominator of $(x - 3) x$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

Reorder the factors of $(x - 3) x$ .

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

Combine the numerators over the common denominator.

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

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

Apply the distributive property.

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

Multiply $3$ by $- 3$ .

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

Add $- x$ and $3 x$ .

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

Multiply the numerator by the reciprocal of the denominator.

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

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

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

Cancel the common factor of $x - 3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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