Question

$\frac{xy}{y - x} = 6$

Answer 1

Xy/(x + y) = 6/5
⇒ (x + y)/xy = 5/6 [ take reverse ]
⇒ x/xy + y/xy = 5/6
⇒ 1/y + 1/x = 5/6 --------(1)

again, xy/(y - x) = 6
⇒(y - x)/xy = 1/6 [ take reverse ]
⇒y/xy - x/xy = 1/6
⇒ 1/x - 1/y = 1/6 -------(2)

add equations (1) and (2) ,
(1/y + 1/x ) + (1/x - 1/y) = 5/6 + 1/6
⇒ 2/x = (5 +1)/6
⇒ 2/x = 1 ⇒ x = 2 , put it in equation (1)

1/y + 1/2 = 5/6
⇒1/y = 5/6 - 1/2 = (5 - 3)/6 = 1/3
⇒ y = 3

Hence, answer is x = 2 and y = 3