Answer
\[ = \frac{{4\,\left( {a + x} \right)}}{{{x^2}{a^2}}}\]
Work Step by Step
\[\begin{gathered}
f\,\left( x \right) = - \frac{4}{{{x^2}}} \hfill \\
\hfill \\
use\,\,the\,\,formula\,\,\frac{{f\,\left( x \right) - f\,\left( a \right)}}{{x - a}} \hfill \\
\hfill \\
\frac{{f\,\left( x \right) - f\,\left( a \right)}}{{x - a}} = \frac{{ - \frac{4}{{{x^2}}} + \frac{4}{{{a^2}}}}}{{x - a}} \hfill \\
\hfill \\
simplify\,\,\,the\,\,\,numerator \hfill \\
\hfill \\
= \frac{{\frac{{ - 4{a^2} + 4{x^2}}}{{{x^2}{a^2}}}}}{{x - a}} \hfill \\
\hfill \\
= \frac{{\frac{{ - 4\,\left( {a - x} \right)\,\left( {a + x} \right)}}{{{x^2}{a^2}}}}}{{x - a}} \hfill \\
\hfill \\
= \frac{{4\,\left( {x - a} \right)\,\left( {a + x} \right)}}{{{x^2}{a^2}\,\left( {x - a} \right)}} \hfill \\
\hfill \\
cancel\,\,x - a \hfill \\
\hfill \\
= \frac{{4\,\left( {a + x} \right)}}{{{x^2}{a^2}}} \hfill \\
\hfill \\
\end{gathered} \]
