Are $x,y$ rational if $x+y$ is rational and $x-y$ is rational?

Question

Are $x,y$ rational if $x+y$ is rational and $x-y$ is rational?

This question was given in maths class, and I don't know where to start. I would be happy if the answer was included in the proof.

Answer 1

The answer is yes, since we have:

$$x = \frac{1}{2} \left( (x+y)+(x-y) \right) $$

$$y = \frac{1}{2} \left( (x+y)-(x-y) \right)$$

So $x$ and $y$ can be expressed as the the sum and product of rational numbers