Question 29972
x = 8/y so that {{{ (1/x) - (1/y) = (1/4) }}} becomes


{{{ (y/8) - (1/y) = (1/4) }}}. Now multiply every term by 8y, to give
{{{ y^2 - 8 = 2y }}}
{{{ y^2 - 2y - 8 = 0 }}}
(y-4)(y+2) = 0


so y-4 = 0 or y+2 = 0
--> y=4 or y = -2


When y=4, so x=8/4 --> x=2
When y=-2, so x=8/-2 --> x=-4


CHECK:
1. for (2,4): {{{ (1/x) - (1/y) }}}
{{{ (1/2) - (1/4) }}}
--> 1/4... correct


2. for (-4,-2): {{{ (1/x) - (1/y) }}}
{{{ (1/-4) - (1/-2) }}}
{{{ (-1/4) + (1/2) }}}
--> 1/4... correct


jon.