(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is to prove that f(x,y) >= g(x,y)

x and y are positive integers

2. Relevant equations

f(x,y) = 1/6 { 2(x-y-2)/(x+2y-2) + 10(x-y+1)/(x+2y+1) }

g(x,y) = 2(x-y)/(x+2y)

3. The attempt at a solution

I'm looking for any general advice on how to approach this question. The approach that I have attempted is to set g(x,y) = k and then to solve for x.

x = -2y(k +1) / (k-2)

Then I substituted this formula back into the equation f(x,y) in the hopes that this would simply to a form that indicates that the inequality is true; however, after doing this a simple solution does not seem to fall out:

f(x,y) = 1/6 { (yk-2y-2k+2)/(-3y-k+2) + 10(-3yk-k-2)/(-6y+k-2))}

Any suggestions to how to approach this kind of problem or on this specific problem would be very appreciated!

Thanks

Dan

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: How do I prove that f(x,y) <= g(x,y)

**Physics Forums | Science Articles, Homework Help, Discussion**