一道指数运算的题目2^x/(2^x-1)-1/2怎么化成1/(2^x-1)+1/2

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一道指数运算的题目
2^x/(2^x-1)-1/2怎么化成1/(2^x-1)+1/2

2^x/(2^x-1)-1/2
=[(2^x-1)+1]/(2^x-1)-1/2
=1+1/(2^x-1)-1/2
=1/(2^x-1)+1/2