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)#?

1 Answer
Jul 21, 2015

Answer:

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)#

Explanation:

#(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)#