一道含有根号的计算题（字母）计算 (x*√x+x*√y)/(xy-y²)-(x+√xy+y

问题补充：

一道含有根号的计算题（字母）计算 (x*√x+x*√y)/(xy-y²)-(x+√xy+y)/（x*√x-y*√y)√是根号,√xy是根号下xy,xy都在根号下面

答案：

设a=√x,b=√y

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

=(a^3+a^2*b)/(a^2*b^2-b^4)-(a^2+ab+b^2)/(a^3-b^3)

=a^2*(a+b)/(b^2(a-b)(a+b)) - (a^2+ab+b^2)/((a-b)(a^2+ab+b^2))

=a^2/(b^2*(a-b)) - (1/(a-b))

=(1/(b^2*(a-b)))*(a^2-b^2)

=(1/(b^2*(a-b)))*(a+b)(a-b)

=(a+b)/b^2

=(√x+√y)/y

======以下答案可供参考======

供参考答案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