Simplify (2x)/(2x-y) - y/(2x+y) - (4xy)/(4x^2-y^2)2x2xyy2x+y4xy4x2y2 ?

1 Answer
Dec 6, 2016

(2x-y)/(2x+y)2xy2x+y Where y!=2xy2x

Explanation:

First consider the first two terms:

(2x)/(2x-y) - y/(2x+y) = (2x(2x+y) - y(2x-y))/ (4x^2-y^2)2x2xyy2x+y=2x(2x+y)y(2xy)4x2y2

Now combine this result with the third term:

(2x(2x+y) - y(2x-y))/ (4x^2-y^2) - (4xy)/(4x^2-y^2)2x(2x+y)y(2xy)4x2y24xy4x2y2

= (4x^2+2xy-2xy+y^2 -4xy)/(4x^2-y^2)=4x2+2xy2xy+y24xy4x2y2

= (4x^2+y^2 -4xy)/(4x^2-y^2)=4x2+y24xy4x2y2

Factorise top and bottom:

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

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

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