Answer
$\frac{x}{x-5}$.
Work Step by Step
The given expression is
$=\frac{\frac{5}{x}+1}{1-\frac{25}{x^2}}$
Divide and multiply the fraction by $x^2$.
$=\frac{x^2}{x^2}\cdot \frac{\frac{5}{x}+1}{1-\frac{25}{x^2}}$
Use the distributive property.
$= \frac{x^2\cdot\frac{5}{x}+x^2\cdot1}{x^2\cdot 1 -x^2\cdot\frac{25}{x^2}}$
Simplify.
$= \frac{5x+x^2}{x^2-25}$
Factor $5x+x^2$.
$=x(5+x)$
$=x(x+5)$
Factor $x^2-25$
Use the algebraic identity $a^2-b^2=(a+b)(a-b)$.
$=(x+5)(x-5)$
Substitute the factor into the fraction as shown below.
$= \frac{x(x+5)}{(x+5)(x-5)}$
Cancel common terms.
$= \frac{x}{x-5}$.
