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#