Prove that a+b is irrational?

okay so the question is: Suppose that a is a rational number and that b is an irrational number. Prove that a+b is irrational.

So i went to prove A: ab is irrational by contradiction, assuming A is false.

Therefore ab is rational, so ab = m/n for integers m and , n is nonzero. So if a is given to be rational then a = k/l for integers k and l, l and k are both nonzero.

So b = m/n + a .... then i completely got lost...

Could someone help me from there, or let me know if I am completely wrong? Thanks.