Question

S = p/(q + p(1 − q)) solve for q

Answer 1

s = p/(q +p -pq)
q +p -pq = p/s
q -pq = p/s - p
q(1-p) = p/s - p
q = (p/s - p) / (1-p)

Answer 2

S = p/(q+p(1-q)) S(q+p(1-q)) = p S(q+p-pq) = p Sq+Sp-Spq = p Sq-Spq = p-Sp q(S-Sp) = p-Sp q = (p-Sp)/(S-Sp)