lim(1/x-1/e^x-1)求极限0/0过程怎么算的详细点谢谢！

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lim[1/x -1/(e^x-1)] (x→0)
=lim{(e^x-1-x)/[x(e^x-1)}(x→0)
=lim[(e^x-1-x)/x^2](x→0)…(因为e^x-1~x)
=lim[(e^x-1)/2x](x→0)…(洛必达法则)
=lim(x/2x)……(又仔模桐念坦码宏用e^x-1~x)
=1/2.

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