Simplify x-9/(x-3)-3

$x - \frac{9}{x - 3} - 3$

Find the common denominator.

Write $x$ as a fraction with denominator $1$ .

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

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

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

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

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

Write $- 3$ as a fraction with denominator $1$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Apply the distributive property.

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

Multiply $x$ by $x$ .

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

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

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

Apply the distributive property.

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

Multiply $- 3$ by $- 3$ .

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

Simplify terms.

Combine the opposite terms in $x^{2} - 3 x - 9 - 3 x + 9$ .

Add $- 9$ and $9$ .

$\frac{x^{2} - 3 x - 3 x + 0}{x - 3}$

Add $x^{2} - 3 x - 3 x$ and $0$ .

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

Subtract $3 x$ from $- 3 x$ .

$\frac{x^{2} - 6 x}{x - 3}$

Factor $x$ out of $x^{2} - 6 x$ .

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

$\frac{x \cdot x - 6 x}{x - 3}$

Factor $x$ out of $- 6 x$ .

$\frac{x \cdot x + x \cdot - 6}{x - 3}$

Factor $x$ out of $x \cdot x + x \cdot - 6$ .

$\frac{x (x - 6)}{x - 3}$