OG - DS - #139

[unique]

if x is not equal to -y

is x-y/x+y > 1

1. x>0
2. y<0

How to solve this w/o picking nos.

[StaceyKoprince]

Without picking numbers? Why would you want to not do that? :)

Given: x is not equal to -y.

Is (x-y)/(x+y) > 1? (I'm going to assume this is how it's supposed to be written, not (x) - (y/x) + (y) > 1, because otherwise why would they tell me x is not equal to -y? Correct me if I'm wrong.)

I can see from my statements that this is going to revolve around whether these guys are positive or negative. So I'll keep that in mind and use logic.

(1) x is positive. Nothing about y, so it could be positive or negative.
- if y is positive, then (x-y) could be positive or negative and (x+y) has to be positive. So the quotient could be -/+ or +/+, so I can't tell if it will be greater than 1. I can stop here - this statement is now insufficient...
- ...but I'll show the other option anyway. If y is negative, then (x-y) must be positive and (x+y) could be positive or negative. Same logic as above, can't tell.

(2) y is negative. Nothing about x, so it could be positive or negative.
- if x is positive, then (x-y) must be positive and (x+y) could be positive or negative. So the quotient could be +/- or +/+, so I can't tell if it will be greater than 1. I can stop here - this statement is now insufficient...
- ...but I'll show the other option anyway. If x is negative, then (x-y) could be positive or negative and (x+y) must be negative. Same logic as above, can't tell.

(1) AND (2). x is positive, y is negative. If this is true, then (x-y) must be positive and (x+y) could be positive or negative. I still can't tell! Argh. E.