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)=0
x=2 , x=-3
The solution is by putting denominator equal to zero.
(x-7)=0
x=7
As 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]
