Solve for f: (1/p)+(1/q)=(1/f)?

f=pq/(p+q)
God bless you.

1/p + 1/q = 1/f
f = 1/(1/p + 1/q)
f = 1/[q/(pq) + p/(pq)]
f = 1/[(q + p)/(pq)]
f = 1[pq/(p + q)]
f = pq/(p + q)

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

multiply by fpq
so the equation will be
fq+fp = pq
f(p+q)=pq
f = pq/(p+q)