Simplify ((x^2-6x+9)/(5x))÷((x-3)/(x+3))

$\frac{x^{2} - 6 x + 9}{5 x} \div \frac{x - 3}{x + 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} - 6 x + 9}{5 x} \cdot \frac{x + 3}{x - 3}$

Step 2

Factor using the perfect square rule.

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

$\frac{x^{2} - 6 x + 3^{2}}{5 x} \cdot \frac{x + 3}{x - 3}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

$\frac{x^{2} - 2 \cdot x \cdot 3 + 3^{2}}{5 x} \cdot \frac{x + 3}{x - 3}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 3$ .

$\frac{{(x - 3)}^{2}}{5 x} \cdot \frac{x + 3}{x - 3}$

Step 3

Simplify terms.

Cancel the common factor of $x - 3$ .

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

$\frac{(x - 3) (x - 3)}{5 x} \cdot \frac{x + 3}{x - 3}$

Cancel the common factor.

$\frac{(x - 3) (x - 3)}{5 x} \cdot \frac{x + 3}{x - 3}$

Rewrite the expression.

$\frac{x - 3}{5 x} (x + 3)$

Multiply $\frac{x - 3}{5 x}$ by $x + 3$ .

$\frac{(x - 3) (x + 3)}{5 x}$