Discrete math direct proof question

[mgk501]

I have a question on my homework that I have no idea how to start. If someone could show me the steps for this problem so I can see how it is done that would be awesome! Thanks

#1.) Prove using a direct proof that for every rational number x, if x ≠ 0, then 1/x is rational

 

[daon2]

I have a question on my homework that I have no idea how to start. If someone could show me the steps for this problem so I can see how it is done that would be awesome! Thanks

#1.) Prove using a direct proof that for every rational number x, if x ≠ 0, then 1/x is rational

The proof is essentially: 1/(a/b) = b/a

The actual step by step proof will depend on your axioms and previous results.