Answer
\[ = - a - x - 4\]
Work Step by Step
\[\begin{gathered}
f\,\left( x \right) = 4 - 4x - {x^2} \hfill \\
\hfill \\
{\text{Derivative formula}} \hfill \\
\hfill \\
\frac{{f\,\left( x \right) - f\,\left( a \right)}}{{x - a}} = \frac{{4 - 4x - {x^2} - 4 + 4a + {a^2}}}{{x - a}} \hfill \\
\hfill \\
factor\,\,and\,\,\,simplify \hfill \\
\hfill \\
= \frac{{{a^2} - {x^2} + 4\,\left( {a - x} \right)}}{{x - a}} \hfill \\
\hfill \\
\frac{{\,\left( {a - x} \right)\,\left( {a + x} \right) + 4\,\left( {a - x} \right)}}{{x - a}} \hfill \\
\hfill \\
= \frac{{\,\left( {a - x} \right)\,\left( {a + x + 4} \right)}}{{x - a}} \hfill \\
\hfill \\
cancel\,\,\,\,x - a \hfill \\
\hfill \\
= - 1\,\left( {a + x + 4} \right) \hfill \\
\hfill \\
multiply \hfill \\
\hfill \\
= - a - x - 4 \hfill \\
\end{gathered} \]
