搜狗做题网化简:((根号x-根号y)^3+2x根号x+y根号y)/(x根号x+y根号y)+(3根号xy-3y)/(x-y)
来源：学生作业帮 编辑：搜狗做题网作业帮 分类：数学作业 时间：2024/04/28 18:12:39
化简:((根号x-根号y)^3+2x根号x+y根号y)/(x根号x+y根号y)+(3根号xy-3y)/(x-y)
题是这样的吧：
[(√x-√y)^3+2x√x+y√y]/(x√x+y√y) + [3√(xy)-3y]/(x-y)
原式=[(x√x-3x√y+3y√x-y√y)+2x√x+y√y]/(x√x+y√y) + [3√(xy)-3y]/(x-y)
=(3x√x-3x√y+3y√x)]/(x√x+y√y) + [3√(xy)-3y]/(x-y)
=3√x[x-√(xy)+3y]/{(√x+√y)[x-√(xy)+3y]}+3√y(√x-√y)/[(√x+√y)(√x-√y)]
=(3√x)/(√x+√y) + (3√y)/(√x+√y)
=(3√x+ 3√y)/(√x+√y)
=3(√x+ √y)/(√x+√y)
=3
这题要用到三次方乘法公式和立方和公式
[(√x-√y)^3+2x√x+y√y]/(x√x+y√y) + [3√(xy)-3y]/(x-y)
原式=[(x√x-3x√y+3y√x-y√y)+2x√x+y√y]/(x√x+y√y) + [3√(xy)-3y]/(x-y)
=(3x√x-3x√y+3y√x)]/(x√x+y√y) + [3√(xy)-3y]/(x-y)
=3√x[x-√(xy)+3y]/{(√x+√y)[x-√(xy)+3y]}+3√y(√x-√y)/[(√x+√y)(√x-√y)]
=(3√x)/(√x+√y) + (3√y)/(√x+√y)
=(3√x+ 3√y)/(√x+√y)
=3(√x+ √y)/(√x+√y)
=3
这题要用到三次方乘法公式和立方和公式
化简:((根号x-根号y)^3+2x根号x+y根号y)/(x根号x+y根号y)+(3根号xy-3y)/(x-y)
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