Question

Find all numbers for which the rational expression is undefined z^2+6/z^2-7z-8

Answer 1

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
`\bf \cfrac{z^2+6}{0}\impliedby unde fined`

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.


`\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}`