Answer
$ x(x+1)$.
Work Step by Step
The given expression is
$\Rightarrow \frac{x}{1-\frac{1}{1+\frac{1}{x}}}$
Solve the lowest denominator.
$=1+\frac{1}{x}$
$=\frac{1}{1}+\frac{1}{x}$
The LCD of the denominators is $x$.
$=\frac{x}{x}+\frac{1}{x}$
$=\frac{x+1}{x}$
Back substitute into the fraction.
$=\frac{1}{\frac{x+1}{x}}$
Invert the divisor and multiply.
$=\frac{x}{x+1}$
Back substitute into the fraction.
$\Rightarrow \frac{x}{1-\frac{x}{x+1}}$
Now solve the denominator.
$=1-\frac{x}{x+1}$
$=\frac{1}{1}-\frac{x}{x+1}$
The LCD of the denominators is $x+1$.
$=\frac{x+1}{x+1}-\frac{x}{x+1}$
$=\frac{x+1-x}{x+1}$
Simplify.
$=\frac{1}{x+1}$
Back substitute into the fraction.
$\Rightarrow \frac{x}{\frac{1}{x+1}}$
Invert the divisor and multiply.
$\Rightarrow \frac{x(x+1)}{1}$.
$\Rightarrow x(x+1)$.
