[
(x-y)^3
×
(√x+√y)^(-3)
+
3(x√y-y√x)
]
/
(x√x+y√y)
=[
(x-y)^3
/(√x+√y)^3
+
3√(xy)
×
(√x-√y)
]
/
(x√x+y√y)
(注：中括弧中第2项提取√(xy)
)
={
[(x-y)/(√x+√y)]^3
+
3√(xy)
×
(√x-√y)
}
/
(x√x+y√y)
(注：第1项中x-y因式分解(√x+√y)(√x-√y)
)
=[
(√x-√y)^3
+
3√xy
×
(√x-√y)
]
/
(x√x+y√y)
(注：把第1项用完全立方展开，再合并整理)
=(x√x-y√y)
/
(x√x+y√y)
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