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

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

A

`(x+1)/(4(x^(2)+1))+(x+5)/(2(x^(2)+1)^(2))-1/(4(x-1))`

B

`(x+1)/(4(x^(2)+1))+(x-5)/(2(x^(2)+1)^(2))-1/(4(x-1))`

C

`(x+1)/(4(x^(2)+1))+(x+5)/(2(x^(2)-1)^(2))-1/(4(x+1))`

D

`(x+1)/(4(x^(2)-1))+(x+5)/(2(x^(2)+1)^(2))-1/(4(x-1))`

Text Solution

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The correct Answer is:
A
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(x^(3))/((2x-1)(x-1)^(2))

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

Knowledge Check

  • 1/((x-3)(x^(2)+1)^(2))=

    A
    `1/(100(x-3))-(x+3)/(100(x^(2)+1))-(x+3)/(10(x^(2)+1)^(2))`
    B
    `1/(100(x+3))-(x+3)/(100(x^(2)+1))-(x+3)/(10(x^(2)+1)^(2))`
    C
    `1/(100(x-3))-(x+3)/(100(x^(2)-1))-(x+3)/(10(x^(2)-1)^(2))`
    D
    `1/(100(x+3))-(x+3)/(100(x^(2)-1))-(x+3)/(10(x^(2)+1)^(2))`

  • Match the following. {:(I." If "(5x^(2)+2)/(x^(3)+x)=A/x+(Bx)/(x^(2)+1) " then "B=, "a) "2), (II." If "(4x)/(x^(2)-1)=A/(x-1)+B/(x+1) " then "A=, "b) "3), (III. " If "(3x+2)/(2-x-x^(2))=A/(2+x)+B/(1-x)" then "A=, "c) "-3//2), (IV." If "(2x+1)/((x-1)(x^(2)+1))=A/(x-1)+(Bx+C)/(x^(2)+1) " then "B=, "d) "-4//3):}

    A
    c, d, a, b
    B
    b, a, d, c
    C
    c, a, b, d
    D
    c, b, a, d

  • underset(x to 1//2)lim {(8x-3)/(2x-1)-(4x^(2)+1)/(4x^(2)-1)}=

    A
    `1//2`
    B
    `1//8`
    C
    `7//2`
    D
    `1//32`

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