Challenging math problem

Question

The product of real numbers x, y, and z is 1. Find all possible values of (1/1+x+xy) + (1/1+y+yz) + (1/1+z+zx).

 

[Side note: The / symbol above indicates a fraction, not division.] 

Answer 1

For starters, I just want to clarify for you that fractions are simply unsolved division problems and thus are not different things.  That's an important concept to understand when looking at fractions.

 

I think the best way to start this problem is to multiply through by (xyz/1) and cancel out.  This should give you a simpler equation and allow you to solve easily with prealgebra methods. 

 

I hope oped that was clear and helps!