# Fraction & Inequality: How to solve for x?

• October 23rd 2009, 07:48 AM
Kataangel
Fraction & Inequality: How to solve for x?
Hi, I've got this horrible fraction to solve for x for:

$-\frac{ln(x+1)}{(x+2)^2}>0$

I don't know the next step to proceed to solve for x. Can anyone help me with it?
• October 23rd 2009, 07:56 AM
Quote:

Originally Posted by Kataangel
Hi, I've got this horrible fraction to solve for x for:

$-\frac{ln(x+1)}{(x+2)^2}>0$

I don't know the next step to proceed to solve for x. Can anyone help me with it?

HI

The denominator is squared , hence it can take any real value of x to be positive . Note there is a negative sign .

The numerator has to be negative .

ln (x+1)<0

Since ln 1 =0 , ln 0 = infinity ,

ln of anything lesser than 1 would be negative .

hence 0<x+1<1

-1<x<0 would be the solution set .