If x4x−1x−2=fx+Ax−1+Bx−2, then

x4x−1x−2=x2+3x+7+15x−14x−1x−2∴fx=x2+3x+7

If x4x−1x−2=fx+Ax−1+Bx−2, then

x4x−1x−2=x2+3x+7+15x−14x−1x−2∴fx=x2+3x+7

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If $\frac{x^{4}}{(x - 1) (x - 2)} = f (x) + \frac{A}{x - 1} + \frac{B}{x - 2}$ , then

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$f (x) = x^{2} - 3 x + 7$

$f (x) = x^{2} + 3 x + 7$

A + B = 17

$A - B = - 18$

answer is B.

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Detailed Solution

$\frac{x^{4}}{(x - 1) (x - 2)}$

$= x^{2} + 3 x + 7 + \frac{15 x - 14}{(x - 1) (x - 2)}$

$∴ f (x) = x^{2} + 3 x + 7$

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If x4x−1x−2=fx+Ax−1+Bx−2, then

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If $\frac{x^{4}}{(x - 1) (x - 2)} = f (x) + \frac{A}{x - 1} + \frac{B}{x - 2}$ , then