Answer
$ 10$.
Work Step by Step
The given expression is
$\Rightarrow \frac{5}{1-\frac{5}{5+x}}-\frac{5}{\frac{5}{5-x}-1}$
Solve the denominator of the first fraction.
$=1-\frac{5}{5+x}$
$=\frac{1}{1}-\frac{5}{5+x}$
The LCD of the denominators is $(5+x)$.
$=\frac{5+x}{5+x}-\frac{5}{5+x}$
$=\frac{5+x-5}{5+x}$
Simplify.
$=\frac{x}{5+x}$
Solve the denominator of the second fraction.
$=\frac{5}{5-x}-1$
$=\frac{5}{5-x}-\frac{1}{1}$
The LCD of the denominators is $(5-x)$.
$=\frac{5}{5-x}-\frac{5-x}{5-x}$
$=\frac{5-(5-x)}{5-x}$
Simplify.
$=\frac{5-5+x}{5-x}$
$=\frac{x}{5-x}$
Back substitute all values into the given fraction.
$\Rightarrow \frac{5}{\frac{x}{5+x}}-\frac{5}{\frac{x}{5-x}}$
Invert the divisor and multiply.
$\Rightarrow 5\cdot \frac{5+x}{x}-5\cdot \frac{5-x}{x}$
$\Rightarrow \frac{5(5+x)}{x}-\frac{5(5-x)}{x}$
Apply the distributive property.
$\Rightarrow \frac{25+5x}{x}-\frac{25-5x}{x}$
$\Rightarrow \frac{25+5x-(25-5x)}{x}$
$\Rightarrow \frac{25+5x-25+5x}{x}$
Simplify.
$\Rightarrow \frac{10x}{x}$
Cancel common terms.
$\Rightarrow 10$.
