What is the sum of $(x + 1)$ and the reciprocal of $(x - 1)$ ?

\frac{2 x}{x - 1}

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\frac{x^{2}}{x - 1}

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\frac{x^{2} - 2}{x - 1}

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\frac{x^{2}}{x^{2} - 1}

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Solution

The correct option is D $\frac{x^{2}}{x - 1}$
Required sum $= (x + 1) + \frac{1}{(x - 1)}$
$= \frac{(x + 1) (x - 1) + 1}{(x - 1)}$
$= \frac{x^{2} + x - x - 1 + 1}{x - 1}$
$= \frac{x^{2}}{x - 1}$

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