Simplify (r/(r-5))÷((r^2)/(r^2-25))

$\frac{r}{r - 5} \div \frac{r^{2}}{r^{2} - 25}$

To divide by a fraction, multiply by its reciprocal.

$\frac{r}{r - 5} \cdot \frac{r^{2} - 25}{r^{2}}$

Simplify terms.

Cancel the common factor of $r$ .

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

$\frac{r}{r - 5} \cdot \frac{r^{2} - 25}{r \cdot r}$

Cancel the common factor.

$\frac{r}{r - 5} \cdot \frac{r^{2} - 25}{r \cdot r}$

Rewrite the expression.

$\frac{1}{r - 5} \cdot \frac{r^{2} - 25}{r}$

Multiply $\frac{1}{r - 5}$ by $\frac{r^{2} - 25}{r}$ .

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

Simplify the numerator.

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

$\frac{r^{2} - 5^{2}}{(r - 5) r}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = r$ and $b = 5$ .

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

Cancel the common factor of $r - 5$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{r + 5}{r}$