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dmcglinn

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## Homework Statement

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

x and y are positive integers

## Homework 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)

## 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

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