Divide (((x+7)^2)/(x-7))/((x^2-49)/(7x-49))

$\frac{\frac{{(x + 7)}^{2}}{x - 7}}{\frac{x^{2} - 49}{7 x - 49}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{{(x + 7)}^{2}}{x - 7} \cdot \frac{7 x - 49}{x^{2} - 49}$

Step 2

Factor $7$ out of $7 x - 49$ .

Factor $7$ out of $7 x$ .

$\frac{{(x + 7)}^{2}}{x - 7} \cdot \frac{7 (x) - 49}{x^{2} - 49}$

Factor $7$ out of $- 49$ .

$\frac{{(x + 7)}^{2}}{x - 7} \cdot \frac{7 x + 7 \cdot - 7}{x^{2} - 49}$

Factor $7$ out of $7 x + 7 \cdot - 7$ .

$\frac{{(x + 7)}^{2}}{x - 7} \cdot \frac{7 (x - 7)}{x^{2} - 49}$

Step 3

Simplify the denominator.

Rewrite $49$ as $7^{2}$ .

$\frac{{(x + 7)}^{2}}{x - 7} \cdot \frac{7 (x - 7)}{x^{2} - 7^{2}}$

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 $b = 7$ .

$\frac{{(x + 7)}^{2}}{x - 7} \cdot \frac{7 (x - 7)}{(x + 7) (x - 7)}$

Step 4

Cancel the common factor of $x + 7$ .

Factor $x + 7$ out of ${(x + 7)}^{2}$ .

$\frac{(x + 7) (x + 7)}{x - 7} \cdot \frac{7 (x - 7)}{(x + 7) (x - 7)}$

Cancel the common factor.

$\frac{(x + 7) (x + 7)}{x - 7} \cdot \frac{7 (x - 7)}{(x + 7) (x - 7)}$

Rewrite the expression.

$\frac{x + 7}{x - 7} \cdot \frac{7 (x - 7)}{x - 7}$

Step 5

Cancel the common factor of $x - 7$ .

Factor $x - 7$ out of $7 (x - 7)$ .

$\frac{x + 7}{x - 7} \cdot \frac{(x - 7) \cdot 7}{x - 7}$

Cancel the common factor.

$\frac{x + 7}{x - 7} \cdot \frac{(x - 7) \cdot 7}{x - 7}$

Rewrite the expression.

$(x + 7) \frac{7}{x - 7}$

Step 6

Multiply $x + 7$ by $\frac{7}{x - 7}$ .

$\frac{(x + 7) \cdot 7}{x - 7}$

Step 7

Move $7$ to the left of $x + 7$ .

$\frac{7 (x + 7)}{x - 7}$