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Resolve the following into partial fract...

Resolve the following into partial fractions.
`(2X^(2)+2x+1)/(x^(3)+x^(2))`

Text Solution

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`Let (2X^(2)+2x+1)/(x^(3)+x^(2))= (2X^(2)+2x+1)/(x^(2)(x+1))= A/x+B/x^(2)+C/(x+1)`
Multiplying with `x^(2) (x+1)`
`2x^(2) + 2x+1= Ax(x+1) + B(x+1)+Cx^(2)`
Put `x = 0, 1 = B`
Put ` x = - 1, 2, -2+1 = C(1) rArr C =1`
Equating the coefficients of `x^(2)` ltbr. ` 2 = A + C rArr A = 2 - C = 2 - 1 = 1`
`therefore (2X^(2)+2x+1)/(x^(3)+x^(2))= 1/x+1/x^(2)+1/(x+1)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PARTIAL FRACTIONS -EXERCISE- 7
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  2. Resolve the following into partial fractions. (x+4)/((x^(2)-4)(x+1))

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  3. Resolve the following into partial fractions. (2X^(2)+2x+1)/(x^(3)+x...

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  4. Resolve the following into partial fractions. (2x+3)/ ((x-1)^(3))

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  5. Resolve the following into partial fractions. (x^(2)-2x+6)/((x-2)^(3...

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  6. Resolve the following into partial fractions. (x^(2)-x+1)/((x+1)(x-1)^...

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  7. Resolve the following into partial fractions. 9/((x-1)(x+2)^(2))

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  8. Resolve the following into partial fractions. 1/((1-2x)^(2)(1-3x)

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  9. Resolve the following into partial fractions. 1/(x^(3)(x+a))

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  10. Resolve the following into partial fractions. (x^(2)+5x+7)/((x-3)^(3...

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  11. Resolve the following into partial fractions. (3x^(2)-8x^(2) + 10)/(...

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  12. Resolve the following into partial fractions. (2x^(2)+3x+4)/((x-1)(x...

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  13. Resolve the following into partial fractions. (3x-1)/((1-x+x^(2))(x+...

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  14. Resolve the following into partial fractions. (x^(2)-3)/((x+2)(x^(2)+...

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  15. Resolve the following into partial fractions. (x^(2)+1)/((x^(2)+x+1)...

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  16. Resolve the following into partial fractions. (x^(3) + x^(2)+1)/ ((x...

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  17. Resolve the following into partial fractions. (x^(2))/ ((x-1)(x-2))

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  18. Resolve the following into partial fractions. (x^(3))/((x-1)(x+2))

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  19. Resolve the following into partial fractions. (x^(3))/((2x-1)(x-1)^(2...

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  20. Resolve the following into partial fractions. (x^(3))/((x-a)(x-b)(x-c...

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