Answer
$\text{The simplified form of the given complex fraction is }\dfrac{2}{x(x+h)}$.
Work Step by Step
$\begin{array}{ l l }
=\dfrac{\dfrac{-2}{x+h} -\left( -\dfrac{2}{x}\right)}{h} & \begin{array}{l}
\mathrm{Apply\ the\ rule\ }\\
\dfrac{-a}{b} =-\dfrac{a}{b}
\end{array}\\
& \\
=\dfrac{\dfrac{-2}{x+h} +\dfrac{2}{x}}{h} & \mathrm{Apply\ the\ rule} \ a-( -b) =a+b.\\
& \\
=\dfrac{\left(\dfrac{-2}{x+h} +\dfrac{2}{x}\right) \cdot x( x+h)}{h\cdot x( x+h)} & \begin{array}{l}
\mathrm{Multiply\ the\ numerator\ }\\
\mathrm{and\ denominator\ of\ the\ }\\
\mathrm{complex\ fraction\ by\ its}\\
\mathrm{LCD\ } \ x( x+h).
\end{array}\\
& \\
=\dfrac{\dfrac{-2}{x+h} \cdot x( x+h) +\dfrac{2}{x} \cdot x( x+h)}{h\cdot x( x+h)} & \begin{array}{l}
\mathrm{Apply\ the\ distributive\ }\\
\mathrm{property.}
\end{array}\\
& \\
=\dfrac{\dfrac{-2x( x+h)}{x+h} +\dfrac{2x( x+h)}{x}}{xh( x+h)} & \mathrm{Multiply.}\\
& \\
=\dfrac{-2x+2( x+h)}{xh( x+h)} & \mathrm{Cancel\ common \space factors.}\\
& \\
=\dfrac{-2x+2x+2h}{xh( x+h)} & \begin{array}{l}
\mathrm{Apply\ the\ distributive}\\
\mathrm{property.}
\end{array}\\
& \\
=\dfrac{2h}{xh( x+h)} & \mathrm{Combine\ like\ terms.}\\
& \\
=\dfrac{2}{x( x+h)} & \mathrm{Cancel\ common \space factors.}
\end{array}$
