Simplify (9-x^2)/(x-3)

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

Step 1

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3$ and $b = x$ .

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

Step 2

Simplify terms.

Cancel the common factor of $3 - x$ and $x - 3$ .

Rewrite $3$ as $- 1 (- 3)$ .

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

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

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Divide $(3 + x) \cdot (- 1)$ by $1$ .

$(3 + x) \cdot (- 1)$

Simplify by multiplying through.

Apply the distributive property.

$3 \cdot - 1 + x \cdot - 1$

Simplify the expression.

Multiply $3$ by $- 1$ .

$- 3 + x \cdot - 1$

Move $- 1$ to the left of $x$ .

$- 3 - 1 \cdot x$

Rewrite $- 1 x$ as $- x$ .

$- 3 - x$