SOLUTION: Solve the inequality {{{x^2-4+(3/x)<0}}}

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Question 979540: Solve the inequality x%5E2-4%2B%283%2Fx%29%3C0
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Common denominator for rational expression arithmetic,

%28x%5E2-4x%2B3%29%2Fx%3C0

Using rational roots theorem to check for roots of the denominator,
the critical x values are system%28%28-1-sqrt%2813%29%29%2F2%2C+1%2C+%28-1%2Bsqrt%2813%29%29%2F2%29.

As decimal approximations, those are system%28-2.30278%2C+1%2C+1.30278%29.
Note also that the inequality is UNDEFINED at x=0.

The value 0 and the three other critical values cut the x-number line into FOUR intervals. Check ANY value in each interval to find if the inequality is true or false in each interval.

What you find should be consistant with this graph of the left side as a FUNCTION:

graph%28300%2C300%2C-3%2C3%2C-5%2C5%2Cx%5E2-4%2B%283%2Fx%29%29