SOLUTION: solve 2x/9-x^2 > 0 write in interval form

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Question 1004077: solve 2x/9-x^2 > 0
write in interval form
Answer by ikleyn(52781) About Me  (Show Source):
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solve 2x/9-x^2 > 0
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%282x%29%2F%289-x%5E2%29 > 0.


Write the left part in the form

%282x%29%2F%28%283-x%29%2A%283%2Bx%29%29 > 0.

It is equivalent to this inequality

%282x%29%2F%28%28x-3%29%2A%28x%2B3%29%29 < 0.     (I changed the sign of one term in the denominator and changed the sign of the inequality).

Now at  x < -3  the left part is negative.  Do you understand why?
                Analyse the sigh of each factor in the numerator and denominator.

In the next interval, -3 < x < 0, the left part is positive.  Do you understand why?
                Analyse the sigh of each factor in the numerator and denominator.

Move this way from left to right through the intervals  (0, 3)  and  (3, infinity).  Make the same analysis for each interval.

In this way you will find the final solution.

For similar problems see the lesson  Solving inequalities for rational functions with numerator and denominator factored into a product of linear binomials  in this site.

Please let me know if you succeed with this exercise.