- #1

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## Homework Statement

Suppose a, b, and c are integers and x, y, and z are nonzero real numbers that satisfy the following equations:

xy/(x+y)=a

xz/(x+z)=b

yz/(y+z)=c

Is x rational? If so, express it as a ratio of two integers.

## Homework Equations

I substituted a lot of equations and I know I need x to equal something. What I got was:

x= abcx/(acx+bcx-abx-abc)

However I don't know how to solve for x (my algebra skills suck... don't ask me how I made it to discrete mathematics...)

## The Attempt at a Solution

I know that if I solve for x, I can basically work out the problem on my own.