How to Solve Rational Inequalities?

[priscilla98]

Homework Statement

Solve (x+2)/(x+1) -2 < 0

Homework Equations

LCD: x + 1

The Attempt at a Solution

(x+2-2x-2)/(x+1) < 0

(-x )/(x+1) < 0

But somehow, I got the wrong answer. The answer is (4, 7]. But I don't know where I went wrong.

 

[priscilla98]

I tried everything I could to answer this problem. Am i right that the lcd is x + 1? Because when i multiply - 2 by x + 1, i end up having to cross out + 2 and -2.

 

[eumyang]

I'm confused because you title this thread "Absolute Value Inequalities," but your problem does not have any absolute value symbols. Can you double check the problem, please? Is the problem this?
\frac{x+2}{x+1} -2 &lt; 0
Because that's what I'm interpreting.

Furthermore, according to WolframAlpha, the solution to what I typed above is
(-∞, -1) U (0, ∞), not (4, 7].69

 

[priscilla98]

Your right, its not absolute inequalities. It's rational equalities.

Okay, thanks a lot for answering this question. I really do appreciate it.