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Evaluate the limit:

$$\lim _{ x\xrightarrow { } { 2 }^{ + } }{ \cfrac { 1 }{ \ln { ( x-1 ) } } } -\cfrac { 1 }{ x-2 } $$

A

$\cfrac{1}{2}$

B

$1$

C

Undefined.

D

$0$

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