Wiskunde Multiple Choice Vraag

$\displaystyle\lim_{x\rightarrow\,6}\frac{\sqrt{2x+4}-4}{6\,-\,x}=$	A. \(1\)
B. \(-\frac12\)
C. \(-\frac18\)
D. \(-\frac14\)
E. \(\frac14\)

$\inline\\\displaystyle\lim_{x\rightarrow\,6}\frac{\sqrt{2x+4}-4}{6\,-\,x}\left(=\frac00\right)\overset{H}{=}\displaystyle\lim_{x\rightarrow\,6}\frac{\sqrt{2x+4}-4}{6\,-\,x}\\=\displaystyle\lim_{x\rightarrow\,6}\frac{(\sqrt{2x+4}-4)(\sqrt{2x+4}+4)}{(6\,-\,x)(\sqrt{2x+4}+4)}=\displaystyle\lim_{x\rightarrow\,6}\frac{2x+4-16}{(6\,-\,x)(\sqrt{2x+4}+4)}\\=\displaystyle\lim_{x\rightarrow\,6}\frac{2(x-6)}{(6\,-\,x)(\sqrt{2x+4}+4)}=\displaystyle\lim_{x\rightarrow\,6}\frac{-2}{\sqrt{2x+4}+4}\\=\frac{-2}{\sqrt{16}+4}=\frac{-2}{4+4}=-\frac14$