The reciprocal of $x+\frac{1}{x}$ is

  • A
    $x-\frac{1}{x}$
  • B
    $\frac{1}{x}+x$
  • C
    $\frac{x}{x^{2}+1}$
  • D
    $\frac{x}{x+1}$

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If $x+\frac{1}{y}=1$ and $y+\frac{1}{z}=1$,then find the value of $z+\frac{1}{x}$.

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