Math Help! Please. . .?

Question

After reviewing the resources above, answer this free response question:

Peter says that the following equations are two ways to write the SAME formula. Solve them both for the same variable to decide whether or not you agree with Peter. Explain how you made your decision, based on solving for variables.


p = (r - 1) &
_____
r


p = r
___
(p + 1)



Answers should look something like this:
I agree / disagree with Peter because when I solved for p / r in the first / second equation, the resulting expressions are the same / different.

Here are my steps and my solutions:

Answer 1

I disagree with Peter because when I solved for p in both equations the resulting expressions are different.

Here are my steps and my solutions:

In the second equation, multiply both sides by (p + 1)
p = r (p + 1)

Distribute r through:
p = rp + r

Subtract rp:
p - rp = r

Factor out a p:
p(1 - r) = r

Divide both sides by (1 - r):
p = r / (1 - r)

In the first equation, multiply both sides by r:
p = r(r - 1)

These are different...

Answer 2

I believe the equations to be
p/r = r-1 , and p/(p+1) = r.
If this is correct, then my solution would go like this:

I believe that Peter is incorrect because when solving for p in both equations , I obtained different results.

FIST EQUATION
p/r= r-1
p= r(r-1)

SECOND EQUATION
p/(p+1)= r
p = (p+1)r = rp+r
p-rp = r
p (1-r) = r
p= r/(1-r)

Sorry Peter