Partial fraction of $2 x^{2} - 3 x 4 / (x - 1)^{3}$ will be of the form

A x + B / (x - 1) + C / (x - 1)^{2} + D / (x - 1)^{3}

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A / (x - 1) + b x + c / (x - 1)^{2} + D / (x - 1)^{3}

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A / (x - 1) + B / (x - 1)^{2} + C / (x - 1)^{3}

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None of the above

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Solution

The correct option is C $A / (x - 1) + B / (x - 1)^{2} + C / (x - 1)^{3}$
Partial fraction of $2 x^{2} - 3 x 4 / (x - 1)^{3}$ will be
$\frac{2 x^{2} - 3 x}{(x - 1)^{3}} = \frac{A}{x - 1} + \frac{B}{(x - 1)^{2}} + \frac{C}{(x - 1)^{3}}$
Option C is correct.

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