Question

求lim x→1[2/（1-x²）－x/（1-x）]怎么算

求极限计算题

Answer 1

方法如下，请作参考：

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Answer 2

lim(x->1) [2/(1-x^2) -x/(1-x)]

通分母

=lim(x->1) [2 - x(1+x)]/[(1-x)(1+x)]

=lim(x->1)  (-x^2-x+2)/[(1-x)(1+x)]

=lim(x->1)  -(x^2+x-2)/[(1-x)(1+x)]

=lim(x->1)  -(x+2)(x-1)/[(1-x)(1+x)]

=lim(x->1)  (x+2)/(1+x)

=(1+2)/(1+1)

=3/2

Answer 3

原式=lim(x->1) [2-x(1+x)]/(1-x^2)
=lim(x->1) (-x^2-x+2)/(1-x^2)
=lim(x->1) (x+2)(x-1)/(x+1)(x-1)
=lim(x->1) (x+2)/(x+1)
=3/2