SOLUTION: Solve the inequality x^2-4+(3/x)< 0 What I have tried: (x^3-4x+3)/x < 0 I do not know how to proceed after this. Thank you in advance

Question 981172: Solve the inequality
x^2-4+(3/x)< 0
What I have tried:
(x^3-4x+3)/x < 0
I do not know how to proceed after this.
Thank you in advance
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

and your correct step giving

This inequality has possibly four critical x values:
0, and whatever are the "roots" of the numerator.

Rational Roots Theorem and Synthetic Division will give only as factor, and then quadratic factor will have roots ;
The other zero is 0, for which the equation is undefined.

Check any value within these five intervals:
(-infinity, -2.3025), the right limit being decimal approximation for irrational;
(-2.3025,0);
(0,1);
(1, 1.3025), again right limit is decimal approximation;
(1.3025, infinity).

Find if the value in the interval makes the original inequality true or false.

Here is a graph of the left member just as a check for your efforts checking in each interval.

A close-up of one area of the graph:

--
What you should find:
(-infinity, -2.3025), False
(-2.3025,0), True;
(0,1), False;
(1, 1.3025), True;
(1.3025, infinity), False
RELATED QUESTIONS
I am curious as how to accurately solve for X in the problem: √3-X(Numerator)... (answered by ankor@dixie-net.com)

How would I solve this inequality? 4x^2-2x<=0 I tried this 2(x^2-x)<=0 but I don't know... (answered by stanbon)

how do I solve this inequality?... (answered by stanbon)

Solve the equation. 4(x-3)=5 I have 4x-3-5=0 I am stuck, I do not know what to do... (answered by solver91311)

Could someone help me? Solve the following equations. Leave radicals in radical... (answered by funmath)

Solve the equation x^3+4x^2-9x-6=0 giving each root in an exact form I do not even... (answered by jsmallt9)

What is the value of x? The equation: x^4+7x^3-8x-56=0 There are two values of x and I... (answered by edjones,richwmiller,josgarithmetic)

I have tried to solve the below equation and would to verify that I am correct in my... (answered by Alan3354)

I need to Solve the equation log3 x^2 - log3(3x+18)=0 log is base 3 tried... (answered by stanbon)