分式计算:(1+1/x)÷[(x+4)/(1-x)-(x²-x-2)/(x²-1)(过程)

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分式计算:(1+1/x)÷[(x+4)/(1-x)-(x²-x-2)/(x²-1)(过程)

(x²-x-2)/(x²-1) = [(x-2)(x+1)]/[(x-1)(x+1)] = (x-2)/(x-1)
故(x+4)/(1-x)-(x²-x-2)/(x²-1)=(2x+2)/(1-x)
(1+1/x)÷(2x+2)/(1-x) =[(1-x)(1+x)]/[x(2x+2)]=(1-x)/2x= (1/x-1)*1/2