Which of the following expressions is equivalent to the expression $\frac{2 x}{x - 1} - \frac{3 x}{x + 1}$ ?

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

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\frac{5 x - x^{2}}{x^{2} - 1}

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- \frac{x}{x - 1}

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\frac{6 x}{x^{2} - 1}

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Solution

The correct option is B $\frac{5 x - x^{2}}{x^{2} - 1}$
Consider $\frac{2 x}{(x - 1)} - \frac{3 x}{(x + 1)}$ and taking L.C.M, we get
$\frac{2 x (x + 1) - 3 x (x - 1)}{(x + 1) (x - 1)}$
$= \frac{2 x^{2} + 2 x - 3 x^{2} + 3 x}{(x + 1) (x - 1)}$
$= \frac{(5 x - x^{2})}{(x^{2} - 1)}$
Hence, option B is correct.

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