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x/((x-1)(x^(2)+1)^(2))=...

`x/((x-1)(x^(2)+1)^(2))=`

A

`1/(4(x-1))-(x-1)/(4(x^(2)+1))+(1+x)/(2(x^(2)-1)^(2))`

B

`1/(4(x+1))-(x+1)/(4(x^(2)+1))+(1+x)/(2(x^(2)-1)^(2))`

C

`1/(4(x-1))-(x+1)/(4(x^(2)+1))+(1-x)/(2(x^(2)+1)^(2))`

D

`1/(4(x+1))-(x-1)/(4(x^(2)+1))+(1-x)/(2(x^(2)+1)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-PARTIAL FRACTIONS-EXERCISE 1
  1. If (ax-1)/((1-x+x^(2))(2+x))=x/(1-x+x^(2))-1/(2+x) " then " a=

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  2. If (3x^(3)-2x^(2)-1)/(x^(4)+x^(2)+1)=(Ax+B)/(x^(2)+x+1)+(Cx+D)/(x^(2)+...

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  3. x/((x-1)(x^(2)+1)^(2))=

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  4. 1/((x-3)(x^(2)+1)^(2))=

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  5. (2x-3)/((x-1)(x^(2)+1)^(2))=

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  6. If (1)/((ax+b)(cx+d))=(A)/(ax+b)+(B)/(cx+d) then (1)/((ax+b)^(2)(cx+d)...

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  7. If (1)/((x-a)(x^(2)+b))=(A)/(x-a)+(Bx+C)/(x^(2)+b) then (1)/((x-a)(x^(...

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  8. To find the coefficient of x^(4) in the expansion of (3x)/((x-2)(x-1))...

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  9. The coefficient of x^(3) " in " (5x+6)/((2+x)(1-x)) is

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  10. If abs(x) lt 1 then the coefficient of x^(2) in the expansion of (3x)/...

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  11. The coefficient of x^(n) in the expansion of (1)/(x^(2)-5x+6)"for"|x|l...

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  12. The coefficient of x^(n) in (x-4)/(x^(2)-5x+6) is

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  13. If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x, th...

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  14. The coefficient of x^(n) " in " x/((x-a)(x-b)) is

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  15. The coefficient of x^(n) in (1)/((1-2x)(1-3x)) is

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  16. For |x| lt 1/5, the coefficient of x^(3) in the expansion of (1)/((1-...

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  17. If the expansion in powers of x of the function (1)/((1-ax)(1-bx)) is ...

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  18. The coefficient of x^(n) " in " 1/((1-x)(1-2x)(1-3x)) is

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  19. The coefficient of x^(n) " in " ((1+x)(1-2x)(1-3x))/((1-x)(1-2x)(1-3x)...

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  20. The coefficient of x^(n) in (x+1)/((x-1)^(2)(x-2)) is

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