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

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify terms.

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

Simplify the numerator.

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

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

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

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

Step 4

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

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