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

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

Text Solution

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We have, `1/(2x^(3)+3x^(2)-3x-2)=1/((x-1)(x+2)(2x+1))`
Let
`1/(2x^(2)+3x^(2)-3x-2)=A(x-1)+B/(x+2)+C/(2x1)`. Then,
`rArr 1=A(x+2)(2x+1)+B(x-1)(2x+1)+C(x-1)(x+)`…………..(i)
Putting `x-1=0` or `x=1` in (i), we get `rArr A=1/9`
Putting `x=-2`, in (i), we obtain `B=1/9`
Putting `x=-1/2`in (i), we obtain `C=-4/9`
`therefore 1/(2x^(3)+3x^(2)-3x-2)=1/((x-1)(x+2)(2x+1))=1/(9(x-1))+1/(9(x+2))-4/(9(2x+1))`
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