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Find the constants a,b,c and d, respecti...

Find the constants `a,b,c` and `d`, respectively, if `(1)/(x^(4)-x)=(a)/(x)+(b)/(x-1)+(cx+d)/(x^(2)+x+1)`.

A

`-1,(1)/(3),(-1)/(2),(-5)/(6)`

B

`-1,(1)/(3),(-1)/(2),(5)/(6)`

C

`1,(1)/(3),(1)/(2),(5)/(6)`

D

None of these

Text Solution

Verified by Experts

`(i)` Simplify L.H.S and R.H.s
`(ii)` Put `x=0` and `1` and obtain the values of `a` and `b`.
`(iii)` Compare the like terms and obtain the values of `c` and `d`.
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PEARSON IIT JEE FOUNDATION-PARTIAL FRACTIONS-Level-2
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  2. Resolve (x+1)/(x^(2)-4) into partical fractions.

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  3. Resolve (x)/((x+1)(x-1)^(2)) into partical fractions.

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  4. Resolve (3x-5)/(x^(2)+3x+2) into partical fractions.

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  5. Resolve (3x+5)/(x^(2)+8x-20) into partical fractions.

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  6. Resolve (ax+b^(2))/(x^(2)-(a+b)^(2)) into partical fractions.

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  7. Find the constants a,b,c and d, respectively, if (1)/(x^(4)-x)=(a)/(x)...

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  8. If (x^(3))/((x-1)(x-2))=Ax+B+(C )/(x-1)+(D)/(x-2), then A,B,C and D, r...

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  9. Resolve (2x^(2)+3)/(x^(4)+8x^(2)+15) into partical fractions.

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  10. Resolve (3x+1)/((x-1)^(2)) into partical fractions.

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  11. If (3x^(2)+14x+10)/(x^(2)(x+2))=(A)/(x)+(B)/(x^(2))+(C )/(x+2), then A...

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  12. If (2x-1)/((x+1)(x^(2)-1))=(A)/(x-1)+(B)/(x+1)+(C )/((x+1)^(2)), then ...

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  13. Resolve (ax-b)/((x+1)^(2)) into partical fractions.

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  14. Resolve (4x^(2)+3x+2)/((x-4)^(3)) into partical fractions.

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  15. Resolve (1)/(x^(2)-7x-18) into partical fractions.

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  16. Resolve (10)/(x^(2)-25) into partical fractions.

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  17. Resolve (2x)/(3(x-1)(x-3)) into partical fractions.

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  18. If (x)/((x+2)(x+3))=(A)/(x+3)+(B)/(x+2), then A-B is =.

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  19. Resolve (5)/((x+2)(x+3)) into partical fractions.

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