now.. if a fraction has a denominator that's 0, the fraction is undefined... so hmm for this to happen to this fraction, then it'd look like [tex]\bf \cfrac{z^2+6}{0}\impliedby unde fined[/tex]
now, for that to happen, well, the denominator must be equal to 0, and that happens when z²-7z-8 = 0... when is that? well, let's check.
[tex]\bf \cfrac{z^2+6}{z^2-7z-8}\\\\
-------------------------------\\\\
z^2-7z-8=0\implies (z-8)(z+1)=0\implies z=
\begin{cases}
8\\
-1
\end{cases}\\\\
-------------------------------\\\\
\boxed{z=8}\qquad \cfrac{z^2+6}{(8)^2-7(8)-8}\implies \cfrac{z^2+6}{64-56-8}\implies \cfrac{z^2+6}{0}
\\\\\\
\boxed{z=-1}\qquad \cfrac{z^2+6}{(-1)^2-7(-1)-8}\implies \cfrac{z^2+6}{1+7-8}\implies \cfrac{z^2+6}{0}[/tex]
