Solving Inequalities: (1/x) + (1/x+1) + (1/x+2) >= 0

[chelser13]

(1/x) + (1/x+1) + (1/x+2) _> 0 (greater than or equal to)

so far i know that one set is (infinity, 1), and (-1, ?) and (-2, ?) i'm not sure i am doing this right. I combined all the problem and ended up with (3x^2 + 6x + 2)/ [x(x + 1)(x + 2)]. i know that there is more to the set for -1 and -2 but i am getting lost on how to continue.

Thanks

 

[Deleted member 4993]

Re: Solving Inequalities

(1/x) + (1/x+1) + (1/x+2) _> 0 (greater than or equal to)

so far i know that one set is (infinity, 1), and (-1, ?) and (-2, ?) i'm not sure i am doing this right. I combined all the problem and ended up with (3x^2 + 6x + 2)/ [x(x + 1)(x + 2)]. i know that there is more to the set for -1 and -2 but i am getting lost on how to continue.

Thanks

3x^2 + 6x + 2 = 0

\(\displaystyle x_{1,2} \, = \frac{-6 \pm \sqrt{12}}{6}\)

Those are part of your critical points. f(x) changes sign around those.

Using graphical calculator - plot f(x). Then it will be clear.