Answer
$\text{Expressions in choices B and C are equivalent to -1}.$
Work Step by Step
$\displaystyle \begin{array}{{>{\displaystyle}l}}
\\
\begin{array}{|c|l|}
\hline
A.) & \begin{array}{ l l }
=\dfrac{x+4-8}{x+4} & \mathrm{Rewrite} \ -4\ \mathrm{as} \ 4\ -\ 8\\
& \\
=\dfrac{x+4}{x+4} -\dfrac{8}{x+4} & \mathrm{Apply\ the\ rule} \ \dfrac{a-b}{c} =\dfrac{a}{c} -\dfrac{b}{c}\\
& \\
=1-\dfrac{8}{x+4} & \mathrm{Simplify} .\
\end{array}\\
& \\
\hline
B.) & \begin{array}{ c l }
=\dfrac{-( x+4)}{x+4} & \mathrm{Factor} \ -1\ \mathrm{out} \ \mathrm{from\ the\ expression\ in\ the\ numerator}\\
& \\
=-\dfrac{x+4}{x+4} & \mathrm{Apply\ the\ rule\ }\dfrac{-a}{b} =-\dfrac{a}{b}\\
& \\
=\boxed{-1} & \mathrm{Apply\ the\ rule} \ \dfrac{a}{a} =1
\end{array}\\
& \\
\hline
C.) & \begin{array}{ l l }
-\dfrac{x-4}{-x+4} & \mathrm{In\ the\ denominator,apply\ the\ commutative\ property}\\
& \\
=\dfrac{x-4}{-( x-4)} & \mathrm{Factor\ -1\ from\ the\ expression\ in\ the\ denominator}\\
& \\
=-\dfrac{x-4}{x-4} & \mathrm{Apply\ the\ rule} \ \dfrac{a}{-b} =-\dfrac{a}{b}\\
& \\
=\boxed{-1} &
\end{array}\\
& \\
\hline
D.) & \begin{array}{ l l }
=\dfrac{x-4}{-( x+4)} & \mathrm{Factor\ } -1\ \mathrm{out\ from\ the\ expression\ in\ the\ denominator}\\
& \\
=-\dfrac{x+4-8}{x+4} & \begin{array}{{>{\displaystyle}l}}
\mathrm{Rewrite} \ -4\ \mathrm{as} \ 4\ -\ 8\ \mathrm{in\ the\ numerator} .\\
\mathrm{Apply\ the\ rule} \ \dfrac{a}{-b} =-\dfrac{a}{b}
\end{array}\\
& \\
=-\left(\dfrac{x+4-8}{x+4}\right) & \mathrm{Place\ parentheses\ around\ the\ fraction}\\
& \\
=-\left(\dfrac{x+4}{x+4} -\dfrac{8}{x+4}\right) & \mathrm{Apply\ the\ rule} \ \dfrac{a-b}{c} =\dfrac{a}{c} -\dfrac{b}{c}\\
& \\
=-\left( 1-\dfrac{8}{x+4}\right) & \mathrm{Simplify\ the\ factor\ of\ one} .\\
& \\
=-1+\dfrac{8}{x+4} & \mathrm{Apply\ the\ distributive\ property\ }
\end{array}\\
\hline
\end{array}
\end{array}$
