You need to use the definition of rational, not assume properties of the rational numbers. Look up our definition of rational (e.g. in the textbook) if you're not sure you remember it.
When you use a definition more than once, make sure to pick fresh names for any variables it introduces.
At the end of the proof, your goal is to prove that a certain quantity is rational. That means you need to get its value into the form of a single fraction. If you have the sum of two fractions, add them together to make one fraction.
In the definition of rational, it is critical that certain variables are integers (not random real numbers). Make sure to explicitly check that they are.