Question

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

Answer 1

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