If $f(x)=x+\log \left(\frac{x-1}{x+1}\right)$ is a well-defined real valued function then $f$ is

• A

  monotonically decreasing function
• Correct answer
  B

  monotonically increasing function
• C

  increasing in $(1, \infty)$ and decreasing in $(-\infty,-1)$
• D

  decreasing in $(1, \infty)$ and increasing in $(-\infty,-1)$

Hence, the correct answer is option: 'B'.