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29: If kn≠ k , and n = 1/k , which of the following expression is equivalent to (1-k)/(1-n)A. -n B. -k C. 1D. k

29 If Kn K And N 1k Which Of The Following Expression Is Equivalent To 1k1nA N B K C 1D K class=

Sagot :

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.

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