# Inequality √(x+2) + 1/x+2 >0

#### gillgill

Can you guys help me solve this inequality

√(x+2) + 1/x+2 >0

thanks

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#### Justin Lazear

Is that

$$\sqrt{x+2} + \frac{1}{x} + 2 > 0$$
or
$$\sqrt{x+2} + \frac{1}{x+2} > 0$$

?

You must be careful with your notation to ensure that there isn't ambiguity!

--J

#### VietDao29

Homework Helper
Hi,
Try to arrange it to:
$$\frac{A}{B} <= 0$$
Or
$$\frac{A}{B} >= 0$$
Where $A = a_{1} \times a_{2} \times a_{3} \times ... \times a_{n}$
and $B = b_{1} \times b_{2} \times b_{3} \times ... \times b_{k}$
Then just simply solve the inequation by drawing a chart to see if each element is positive or negative or zero. And finally, see if $$\frac{A}{B}$$ is positive or negative or zero in each case.
Hope this help,
Viet Dao,

#### gillgill

o..icic..thx...
do you have to do the "cases" for it?

#### dextercioby

Homework Helper
You may wanna begin by stating clearly the domain of the "x"...And then look for those "x" which would satisfy your inequation.

Daniel.

#### primarygun

If the question is designed as "equal or bigger",it is more tricky.

#### The Bob

I still want to know what √(x+2) + 1/x+2 >0 is.

How we decided yet???

Is it:

$$\sqrt{\frac{(x + 2) + 1}{x + 2}} > 0$$

Is it:

$$\sqrt{(x + 2) + \frac{1}{x + 2}} > 0$$

or something else???

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