limx→3(1/x-3 – 27/x的3次方-27)怎么做

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limx→3(1/x-3–27/x的3次方-27)怎么做limx→3(1/x-3–27/x的3次方-27)怎么做limx→3(1/x-3–27/x的3次方-27)怎么做1/(x-3)-27/(x

limx→3(1/x-3 – 27/x的3次方-27)怎么做
limx→3(1/x-3 – 27/x的3次方-27)怎么做

limx→3(1/x-3 – 27/x的3次方-27)怎么做
1/(x-3)-27/(x³-27)=【(x²+3x+9)-27】/(x³-27)=(x²+3x-18)/(x³-27)=(x+6)(x-3)/(x-3)(x²+3x+9)=(x+6)/(x²+3x+9)
所以当x→3时,lim【1/(x-3)-27/(x³-27)】=(3+6)/(9+3*3+9)=1/3