Resolve `(2x+1)/((x-1)(x^(2)+1))` into partial fractions.

1.	Resolve `(2x+1)/((x-1)(x^(2)+1))` into partial fractions.
Answer» Equating the like powers of x on both sides of (i) , we get `A+B=0,C-B=2 and A-C=1` On solving these equations , we get `A=(3)/(2),B=(-3)/(2)and C=(1)/(2).` `therefore (2x+1)/((x-1)(x^(2)+1))=(3)/(2(x-1))+(((-3)/(2)x+(1)/(2)))/(x^(2)+1)=[(3)/(2(x-1))+((1-3x))/(2(x^(2)+1))].`

Discussion

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