solve x/x+1

Question

solve x/x+1 < x/x-1

katherinesmith · Answer

$$\frac{ x }{ x + 1 } < \frac{ x }{ x-1 }$$

anonymous · Answer

First multiply either side by the denominators

katherinesmith · Answer

$$\frac{ x }{ (x + 1)(x-1) } < \frac{ x }{ (x-1)(x+1) }$$

anonymous · Answer

When you multiply something the stuff goes on top so you get$$\frac{ x(x-1)(x+1) }{ x+1 }<\frac{ x(x-1)(x+1) }{ x-1 }$$, are you following me?

katherinesmith · Answer

yes... can you do the next step so i can see where you're going with it and then i'll try

anonymous · Answer

Then you cancel stuff out and you get $$x(x-1)<x(x+1)$$

katherinesmith · Answer

x^2 - x < x^2 + x

anonymous · Answer

Hold right there! While that is correct and you can do it that way there is an easier way.  What's on both sides that could cancel out?

katherinesmith · Answer

on both sides of what you put or both sides of what i put?

anonymous · Answer

What I put

katherinesmith · Answer

the x can cancel so you get (x-1) < (x+1)

anonymous · Answer

Exactly! Nice.  Now what can you do?

katherinesmith · Answer

x - 1 < x + 1... not sure how to finish this out

anonymous · Answer

Well you want to get rid of the x on one of he sides so subtract it from both sides and what are you left with

katherinesmith · Answer

-1 < 1 ?

anonymous · Answer

Yep.  And -1 is always less than 1, so no matter what x is -1<1 so x can be any number

katherinesmith · Answer

-1 < x < 0 or x > 1 -1 < x < 0 x > 1 0 < x < 1 those are my options

anonymous · Answer

Hmm.

anonymous · Answer

Answer a makes the most sense but let me figure out the steps to get there

anonymous · Answer

Okay so I see what I did wrong... My bad.  You should start by subtracting the right side from the left side

katherinesmith · Answer

i'm just giving up on this . thanks for the help anyway

anonymous · Answer

:( Okay sorry i couldn't be of more help