计算:√xy+√x/y-√y /x+√(x/y+y/x+2) x＞0，y＞0
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:√xy+√x/y-√y /x+√(x/y+y/x+2)
=√xy+1/y√xy-1/x√xy+√(x²+y²+2xy)/xy
=√xy+1/y√xy-1/x√xy+√(x+y)²/xy
=√xy+1/y√xy-1/x√xy+(x+y)/xy√xy
=√xy+1/y√xy-1/x√xy+1/y√xy+1/x√xy
=√xy+2/y√xy
=√xy+1/y√xy-1/x√xy+√(x²+y²+2xy)/xy
=√xy+1/y√xy-1/x√xy+√(x+y)²/xy
=√xy+1/y√xy-1/x√xy+(x+y)/xy√xy
=√xy+1/y√xy-1/x√xy+1/y√xy+1/x√xy
=√xy+2/y√xy
追问
√(x+y)²/xy=(x+y)/xy√xy？
追答
√(x+y)²/xy=(x+y)/xy√xy
是的
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