Question 529480
{{{(2-(x+y)/(x-2y)) / (2/(x+y) - 1/(x-2y))}}}
Perform the necessary operations to put both expression over a single denominator
{{{(2(x-2y)-(x+y))/(x-2y))}}}
--------------------
{{{(2(x-2y)-(x+y))/((x+y)(x-2y))}}}
:
{{{((2x-4y-x-y))/(x-2y))}}}
--------------------
{{{((2x-4y-x-y))/((x+y)(x-2y))}}}
combine like terms
{{{((x-5y))/(x-2y))}}}
--------------------
{{{((x-5y))/((x+y)(x-2y))}}}
invert the dividing fraction and multiply
{{{((x-5y))/(x-2y))}}} * {{{((x+y)(x-2y))/((x-5y))}}}
Hey! we can cancel: (x-5y) and (x-2y), left with
(x + y)