Explanation

Factor the denominator: x√y+y√x = √(xy)(√x+√y), and x-y = (√x-√y)(√x+√y). The left side becomes (√x-√y)/√(xy) = 1/√y-1/√x. Setting this equal to 1/√x gives 1/√y = 2/√x, so √x = 2√y and x/y = 4 (verified by substitution). Key disputed: a widely circulated third-party Set-A key lists A, but the algebra gives x = 4y. Hence the keyed option is C.