百度作业网一道数学题,计算题 如下图所示
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/04/26 06:26:21
一道数学题,计算题 如下图所示
(x√x+x√y)/(xy-y^2)-(x+√xy+y)/(x√x-y√y)
=x(√x+√y)/y(x-y)-(x+√xy+y)(x√x+y√y)/(x√x-y√y)(x√x+y√y)
=x(√x+√y)/y(x-y)-(x^2+xy+y^2)(√x+√y)/(x^3-y^3)
=x(√x+√y)/y(x-y)-(x^2+xy+y^2)(√x+√y)/(x-y)(x^2+xy+y^2)
=x(√x+√y)/y(x-y)-(√x+√y)/(x-y)
=[x(√x+√y)-y(√x+√y)]/y(x-y)
=(x-y)(√x+√y)/y(x-y)
=(√x+√y)/y
这已经是最简形式了
=x(√x+√y)/y(x-y)-(x+√xy+y)(x√x+y√y)/(x√x-y√y)(x√x+y√y)
=x(√x+√y)/y(x-y)-(x^2+xy+y^2)(√x+√y)/(x^3-y^3)
=x(√x+√y)/y(x-y)-(x^2+xy+y^2)(√x+√y)/(x-y)(x^2+xy+y^2)
=x(√x+√y)/y(x-y)-(√x+√y)/(x-y)
=[x(√x+√y)-y(√x+√y)]/y(x-y)
=(x-y)(√x+√y)/y(x-y)
=(√x+√y)/y
这已经是最简形式了