SOLUTION: Find the solution set for each rational inequalities below. Graph the solution set on a number line. a) (x+3)(x-2) / (x+2)(x-1) >_ 0

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Question 1046372: Find the solution set for each rational inequalities below. Graph the solution set on a number line.
a) (x+3)(x-2) / (x+2)(x-1) >_ 0
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
(x+3)(x-2) / (x+2)(x-1) >_ 0
My guess is that what you wrote is not the inequality which you really have.

Maybe you really have ((x+3)(x-2))/((x+2)(x-1)) >=0
and the rendering makes to appear as
.


The critical values of x are those at which the sign of a factor changes. The critical x values here are -3, -2, 2, 1.
These values cut the real number line into the five intervals:
.


What you do is test ANY value in each interval to find if it makes the expression GREATER THAN OR EQUAL TO 0. Best done as watching the sign of each factor of the expression. 
 

                   Pick Value         SIGNS           RESULT SIGN        MEANS

(-inf,-3]           -4             (- -)/(- -)           +               TRUE

[-3,-2]             -5/2          (+ -)/(- -)            -               FALSE

[-2,1]              -1            (+ -)/(+ -)            +               TRUE

[1,2]               +3/2          (+ -)/(+ +)            -               FALSE

[2,infin)           +3            (+ +)/(+ +)            +               TRUE


Note that "0" would be just as good for TRUTH as "POSITIVE", because the given inequality is for the expression GREATER than or EQUAL to zero. Positive means greater than zero.
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
See the lesson
    - Solving inequalities for rational functions with numerator and denominator factored into a product of linear binomials
in this site.

Similar problem was solved there specially for you with detailed explanations on how to solve it.


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