Write a formal proof for the following statement using proof

Write a formal proof for the following statement using proof by contradiction.

Statement\" For all nonzero real numbers x and ym if x is rational and y is irrational, then x/y is irrational.

Solution

Suppose x/y is rational.
Then (x/y)*y must be irrational, since it\'s one rational number multiply by irrational.
However, we know (x/y)*y = x, which is rational.
This is a contradiction.
Hence, x/y is irrational.