Simplify $(2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)$ ?

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Answer 1 · 2016-12-06T02:52:18

$(2x-y)/(2x+y)$ Where $y!=2x$

First consider the first two terms:

$(2x)/(2x-y) - y/(2x+y) = (2x(2x+y) - y(2x-y))/ (4x^2-y^2)$

Now combine this result with the third term:

$(2x(2x+y) - y(2x-y))/ (4x^2-y^2) - (4xy)/(4x^2-y^2)$

$= (4x^2+2xy-2xy+y^2 -4xy)/(4x^2-y^2)$

$= (4x^2+y^2 -4xy)/(4x^2-y^2)$

Factorise top and bottom:

$=((2x-y)(2x-y))/((2x+y)(2x-y))$

$=(cancel((2x-y))(2x-y))/((2x+y)*cancel((2x-y)))$ Where $2x-y !=0$

$=(2x-y)/(2x+y)$ Where $y!=2x$

Simplify (2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)(2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2) ?