Fibonacci, proof with induction

Hello, I think I am getting stuck; I would really appreciate any help or advice!

Prove by induction that for

To start , prove the base case of :

so

Now assume is true.

We can multiply both sides by to get the term on the right side.

This is where I think I'm not sure about what to do. What I had been thinking is: now try to show that

so that we can conclude with .

I had been trying: It's true that . If we add to both sides, we can get the n+2 term on the left. But then I wasn't sure if there is another step..? Or if I'm on the right track at all?

THANKS! for any help!!