The expression if given as,
[tex]\frac{1-k}{1-n}[/tex]
The condition is given as,
[tex]n=\frac{1}{k}[/tex]
Substitute this value in the expression,
[tex]=\frac{1-k}{1-\frac{1}{k}}[/tex]
Resolve the rational expression as,
[tex]\begin{gathered} =\frac{1-k}{(\frac{k-1}{k})} \\ =\frac{k(1-k)}{k-1} \\ =\frac{-k(k-1)}{k-1} \end{gathered}[/tex]
Cancelling out the common factor,
[tex]\begin{gathered} =\frac{-k(1)}{(1)} \\ =-k \end{gathered}[/tex]
Thus, the simplified form of the given expression is obtained as,
[tex]-k[/tex]
Therefore, option B is the correct choice.
