Please do not copy the solution from Chegg. Tutors here keep doing that. I reported them all. The hint that instructor gave to us is to differentiate both sides by y, then left side I obtain -fY(y), how about right side? Can you go from here?

Frailty. Let X, Y be independent, positive, continuous random variables, such that 1 - Fy(y) = (1 - Fx(y)) fory > 0. The positive number A may be called the frailty or proportional hazard. In more general models, A may itself be a random variable. Show that A P(X > Y) = AP(Y > X) = 1+x