\(A=-\dfrac{1}{x}+\dfrac{1}{x-1}-\dfrac{1}{x-1}+\dfrac{1}{x-2}-...-\dfrac{1}{x-5}+\dfrac{1}{x-6}\)
\(=\dfrac{1}{x-6}-\dfrac{1}{x}=\dfrac{x-x+6}{x\left(x-6\right)}=\dfrac{6}{x\left(x-6\right)}\)
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