Answer:The solution of the expression lies in [tex](-\infty,-3)\cup (2,7)[/tex]Step-by-step explanation:Given : Expression [tex]\frac{x^2+x-6}{x-7}<0[/tex]To find : What is the solution of teh expression ?Solution : Expression [tex]\frac{x^2+x-6}{x-7}<0[/tex]First we factor the numerator,[tex]\frac{(x-2)(x+3)}{x-7}<0[/tex]The solution is by putting numerator equal to zero.(x-2)(x+3)=0(x-2)=0 , (x+3)=0x=2 , x=-3The solution is by putting denominator equal to zero.(x-7)=0x=7As at x=7 the function is not defined.The domain for the above inequality is [tex](-\infty,7)\cup (7,\infty)[/tex]For each root we create a test,For x<-3 it is true.For -3<x<2 it is not true.For [tex]-\infty<x<-3[/tex] it is true.For 2<x<7 it is true.The solution of the expression lies in [tex](-\infty,-3)\cup (2,7)[/tex]