题目

化简（y根号x+x根号y）/（xy-y²）-（x+根号xy+y）/（x根号x-y根号y）.

提问时间：2020-06-24

答案

(y√x+x√y)/(xy-y²)-(x+√xy+y)/(x√x-y√y)
=√xy(√x+√y)/[y(√x+√y)(√x-√y)]-(x+√xy+y)/[(√x-√y)(x+√xy+y)]
=√xy/[y(√x-√y)]-1/(√x-√y)
=√xy/[y(√x-√y)]-y/[y(√x-√y)]
=(√xy-y)/[y(√x-√y)]
=√y(√x-√y)[y(√x-√y)]
=√y/y
用到的一个重要公式：x³-y³=(x-y)(x²+xy+y²)