How do you simplify #(x-y)/(x+y)*(x^2+2xy+y^2)/(x^2-2xy+y^2) div (x^2-y^2)/( x^2-2xy+3y^2)#?

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Answer 1 · 2015-07-21T21:57:16

Resolve into linear factors, cancel factors common to numerator and denominator and simplify to find:

#(x-y)/(x+y)*(x^2+2xy+y^2)/(x^2-2xy+y^2)-:(x^2-y^2)/(x^2-2xy+3y^2)#

#=1-(4y^2)/((x-y)^2)#

#(x-y)/(x+y)*(x^2+2xy+y^2)/(x^2-2xy+y^2)-:(x^2-y^2)/(x^2-2xy+3y^2)#

#=(x-y)/(x+y) * (x^2+2xy+y^2)/(x^2-2xy+y^2) * (x^2-2xy+3y^2)/(x^2-y^2)#

#=((x-y)(x^2+2xy+y^2)(x^2-2xy+3y^2))/((x+y)(x^2-2xy+y^2)(x^2-y^2))#

#=((x-y)(x+y)(x+y)(x+y)(x-3y))/((x+y)(x-y)(x-y)(x-y)(x+y))#

#=((x+y)(x-3y))/((x-y)(x-y))#

#=(x^2-2xy-3y^2)/(x^2-2xy+y^2)#

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

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

#=1-(4y^2)/((x-y)^2)#