Q on q16 of MGMAT Question Bank - Equations, Inequalities&VI

[georginafleming]

Question no. 16 from MGMAT Question Bank - Equations, Inequalities, & VIC's:

If x and y are nonzero integers, is (x-1 + y-1)-1 > [(x-1)(y-1)]-1 ?

(1) x = 2y

(2) x + y > 0

MY QUESTION:
We can simplify the equation above to: does (xy/x+y) > xy? (which is what MGMAT does), but doesn't this then get simplified to (1/x+y)>1? And isn't 1/x+y NEVER bigger than 1, which answers the question without even looking at answer choices 1 or 2?

Please advise, thanks!

[georginafleming]

I think I just found the answer to my own question: I can only divide both sides by xy if I know whether or not xy is 0, negative or positive, correct?

[jnelson0612]

I think I just found the answer to my own question: I can only divide both sides by xy if I know whether or not xy is 0, negative or positive, correct?

Right, looks good to me! :-)