Divide (((x+3)^2)/(x-3))/((x^2-9)/(3x-9))

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Factor $3$ out of $3 x - 9$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 9$ .

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

Factor $3$ out of $3 x + 3 \cdot - 3$ .

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

Step 3

Simplify the denominator.

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

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

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 $b = 3$ .

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

Step 4

Cancel the common factor of $x + 3$ .

Factor $x + 3$ out of ${(x + 3)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $x - 3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

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

Step 7

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

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