Question 932610

{{{(q^2+3q-4)/(q^2-7q-8 )}}} first factor completely 

{{{(q^2-q+4q-4)/(q^2+q-8q-8 )}}} 

{{{((q^2-q)+(4q-4))/((q^2+q)-(8q+8) )}}}

{{{(q(q-1)+4(q-1))/(q(q+1)-8(q+1) )}}}

{{{((q+4)(q-1))/((q+1)(q-8))}}}


domain: all values of {{{q}}} except those which make denominator equal to {{{0}}}

{{{(q+1)(q-8)=0}}} if {{{(q+1)=0}}} or {{{(q-8)=0}}}

{{{(q+1)=0}}} if {{{q=-1}}}

{{{(q-8)=0}}} if {{{q=8}}}

so, these values are excluded from domain, and domain is

{ {{{q}}} element {{{R}}} : {{{q<>-1}}} and {{{q<>8}}} }
(assuming a function from reals to reals)

and your answer is B. {{{q}}} "not equal to" {{{-1}}} and {{{q}}} "not equal to" {{{8}}}