Question 35691
To solve for either x or y, the first step is to clear the fractions by  multiplying both sides by the LCD which is {{{2xy}}}


{{{1/x + 1/y = 1/2}}}
{{{2xy*(1/x) + 2xy*(1/y)  = 2xy*(1/2)}}}

{{{2y + 2x = xy }}}


Now, to solve for x, get all the x terms on one side by subtracting 2x from each side:
{{{2y = xy - 2x}}}


Factor the x, so as to get the x's all in one place:
{{{2y = x(y-2) }}}


Divide both sides by (y-2):
{{{(2y)/(y-2) = (x*(y-2))/(y-2)}}}
{{{(2y)/(y-2) = x}}}


NOW, to solve for y in terms of x, go back to the equation {{{2y + 2x = xy }}}.

To solve for y, get all the y terms on one side by subtracting 2y from each side:
{{{2x = xy - 2y}}}


Factor the y, so as to get the y's all in one place:
{{{2x = y(x-2) }}}


Divide both sides by (x-2):
{{{(2x)/(x-2) = (y*(x-2))/(x-2)}}}
{{{(2x)/(x-2) = y}}}


R^2 at SCC