How to find q for this problem ?

Question

1/p +1/q = 1/r 

 

I got this question wrong on a test and wanna know where I went wrong. What I did was find the common denominator which is pqr and then did cancelling/multiplying. I wasnt too confident in my answer but now wanna know how it's properly done.

Answer 1

(q+p)/(pq) = 1/r

 

Cross multiply, yielding rq + rp = pq

rp = pq - rq

 

rp = q(p-r)

 

q = (rp)/(p-r)