SOLUTION: How do i do this question: (x-2)(x+3)/(x-4)

SOLUTION: How do i do this question: (x-2)(x+3)/(x-4) > 0

Question 26497: How do i do this question:
(x-2)(x+3)/(x-4) > 0
Found 2 solutions by stanbon, venugopalramana:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 Cheers,
Stan H.

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
(x-2)(x+3)/(x-4) > 0
FOR A FRACTION TO BE POSITIVE ,BOTH N.R AND D.R SHOULD BE POSTIVE OR NEGATIVE
CASE I....N.R AND D.R POSITIVE
FOR PRODUCT OF 2 FACTORS TO BE POSITIVE BOTH SHOUD BE POSITIVE OR NEGATIVE.
VARIANT I
X-2,X+3 ARE POSITIVE.SO X>2..D.R=X-4....X-4>0...SO X>4
THAT IS IN THIS CASE X>4
--------------------------
VARIANT II
X-2,X+3 ARE NEGATIVE.SO X<-3....D.R=X-4.....X-4>0...SO X>4...THIS IS NOT POSSIBLE
------------------------------------------------------------------------------
SO UNDER CASE I,THE ONLY POSSIBILITY IS X>4
************************************************
CASE II........N.R AND D.R NEGATIVE.........
FOR PRODUCT OF 2 FACTORS TO BE NEGATIVE ONE SHOUD BE POSITIVE AND ANOTHER NEGATIVE.
SO X SHOULD BE BETWEEN 2 AND -3....AND D.R=X-4<0...X<4
SO X IS BETWEEN 2 AND -3
-----------------------------------------
hence the total solution set is for
x to be greater than 4 or between 2 and -3.
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