Question

x√x+x√y)/(xy-y2)-(x+√xy+y)/(x√x-y√y)化简

Answer 1

令x^1/2=z,y^1/2=w,

原式=(z^3+z^2w)/(z^2w^2-w^4)-(z^2+zw+w^2）/(z^3-w^3)

=(z^3+z^2w-w^3-w^2z)/(z^2w^2-w^4)

=[(z^3-w^3)+(z^2w-w^2z)]/(z^2w^2-w^4)

=(z^2+2zw+w^2)(z-w)/w^2(z-w)(z+w)

=(z+w)/w^2

=(√x+√y)/y