The partial fraction of $$x2x-13x-2$$ are

Correct option is 3-1x-13+-3x-12+-4x-1+4x-2

Questions

The partial fraction of $\frac{x^{2}}{{(x - 1)}^{3} (x - 2)}$ are

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-1x-13+3x-12-4x-1+4x-2

-1x-13-3x-12+4x-1+4x-2

-1x-13+-3x-12+-4x-1+4x-2

None of these

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detailed solution

Correct option is C

Put the repeated factorx-1=y⇒x=y+1∴x2x-13x-2=1+y2y3y-1=1+2y+y2 y3-1+yDividing the numerator,1+2y+y2 by -1+y till y3 appears as factor,we get 1+2y+y2-1+y=(-1-3y-4y2)+4y3-1+yGiven expression =-1y3-3y2-4y+4-1+y=-1x-13+-3x-12+-4x-1+4x-2

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The partial fraction of x2x-13x-2 are

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The partial fraction of $\frac{x^{2}}{{(x - 1)}^{3} (x - 2)}$ are