I understand that in order to solve, i would divide by the highest power of x. But what is he doing here that gives 7/7 for x > -infinity?
if i'm not mistaking your b question doesn't look right.
$\displaystyle \lim_{x \rightarrow \infty } \frac{7-\exp x }{7+8\exp x } $= $\displaystyle \lim_{x \rightarrow \infty } \frac{\exp x( \frac{7 }{\exp x }-1) }{\exp x( \frac{ 7}{\exp x }+8) }$ = $\displaystyle \lim_{x \rightarrow \infty } \frac{( \frac{7 }{\exp x }-1) }{( \frac{ 7}{\exp x }+8) }$$\displaystyle = -\frac{ 1}{8 } $