Simplify (((x+5)^2)/(x-5))/((x^2-25)/(5x-25))

$\frac{\frac{{(x + 5)}^{2}}{x - 5}}{\frac{x^{2} - 25}{5 x - 25}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{{(x + 5)}^{2}}{x - 5} \cdot \frac{5 x - 25}{x^{2} - 25}$

Step 2

Factor $5$ out of $5 x - 25$ .

Factor $5$ out of $5 x$ .

$\frac{{(x + 5)}^{2}}{x - 5} \cdot \frac{5 (x) - 25}{x^{2} - 25}$

Factor $5$ out of $- 25$ .

$\frac{{(x + 5)}^{2}}{x - 5} \cdot \frac{5 x + 5 \cdot - 5}{x^{2} - 25}$

Factor $5$ out of $5 x + 5 \cdot - 5$ .

$\frac{{(x + 5)}^{2}}{x - 5} \cdot \frac{5 (x - 5)}{x^{2} - 25}$

Step 3

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

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

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 $b = 5$ .

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

Step 4

Simplify terms.

Cancel the common factor of $x + 5$ .

Factor $x + 5$ out of ${(x + 5)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 5$ .

Factor $x - 5$ out of $5 (x - 5)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move $5$ to the left of $x + 5$ .

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