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Greatest Binomial Coefficients

Number of Par...

Question

Number of Partial Fractions obtained from: $\frac{1}{x^{4} (x^{3} + 1)}$

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Solution

$\frac{1}{x^{4} (x^{3} + 1)} = \frac{1}{x^{4} (x + 1) (x^{2} - x + 1)}$
$= \frac{A}{x} + \frac{B}{x^{2}} + \frac{C}{x^{3}} + \frac{D}{x^{4}} + \frac{E}{x + 1} + \frac{F x + G}{x^{2} - x + 1}$
$∴$ Number of partial fractions $= 6$

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