(x+y/x-y+x-y/x+y):(x+y/x-y-x-y/x+y)*x^2y^2/(x-y)^2+(x+y)^2

Question

(x+y/x-y+x-y/x+y):(x+y/x-y-x-y/x+y)*x^2y^2/(x-y)^2+(x+y)^2

Answer 1

1.(x+2y)(x-y)=x^2-xy+2xy-2y^2=x^2+xy-2y^2=4 => xy=4-x^2+2y^2(x+2y)(x+y)=x^2+xy+2xy+2y^2=x^2+3xy+2y^2=12

x^2+3(4-x^2+2y^2)+2y^2=12
x^2+12-3x^2+6y^2+2y^2-12=0
-2x^2+8y^2=0
-2(x^2-4y^2)=0
x=2 y=1