Question 26497
You need to look at the equality (x-2)(x+3)/(x-4)=0
This equality is zero if x=2 or x=-3 and is undefined at x=4.
Now, draw a number line and plot -3,2,and 4 on the line.
The three points determine 4 intervals on the line.
(-indef,-3), (-3,2), (2,4), and (4,+indef)
You need to check your inequality with a number in 
each of these intervals.
For example: 
Choose x= -10 in the 1st interval.
Your inequality becomes (-12)(-7)/(-14)<0. Therefore that
interval is not part of your solution.
Choose x=0 in the 2nd interval.
Your inequlity becomes (-2)(3)/(-4)>0. Therefore every
x-value in that interval satisfies your inequality and
constitutes part of your solution.
Do the same for a number in the 3rd interval and a number
in the 4th interval.
You should find that the solution to your inequality is
All values of x in -3<x<2 and in 4<x<+indef.

Cheers,
Stan H.