How to find the solutions of some fractional equations ?

[Chriszz]

Homework Statement

The problem is defined as below.

A/B = x/y

; A/B and x/y are rational numbers.

In some equations, we want to find solutions of variable x and y.
A, B : given constants. integers.
x, y : variables. integers.

Homework Equations

The Attempt at a Solution

 

[ShayanJ]

x=cA and y=cB for any c.

 

[HallsofIvy]

For any integer c. But the point is that given any integers A and B, there are infinite pairs of integers x and y such that \frac{x}{y}= \frac{A}{B}.

 

[thelema418]

For any integer c. But the point is that given any integers A and B, there are infinite pairs of integers x and y such that \frac{x}{y}= \frac{A}{B}.

If you do that you should state something about the case $c = 0$. The result that $x = 0, y = 0, A = 1, B = 2$ is probably not appropriate.