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The partial fractions of fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction are

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  1. fraction numerator 1 over denominator 8 x end fraction minus fraction numerator 1 over denominator 4 x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator 2 x to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator 8 left parenthesis x plus 2 right parenthesis end fraction    
  2. fraction numerator 1 over denominator 8 x end fraction plus fraction numerator 1 over denominator 4 x to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 2 x to the power of 3 end exponent end fraction plus fraction numerator 1 over denominator 8 left parenthesis x plus 2 right parenthesis end fraction    
  3. fraction numerator 1 over denominator 8 x end fraction minus fraction numerator 1 over denominator 4 x to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 2 x to the power of 3 end exponent end fraction minus fraction numerator 1 over denominator 8 left parenthesis x plus 2 right parenthesis end fraction    
  4. fraction numerator 1 over denominator 8 x end fraction plus fraction numerator 1 over denominator 4 x to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 2 x to the power of 3 end exponent end fraction minus fraction numerator 1 over denominator 8 left parenthesis x plus 2 right parenthesis end fraction    

    Answer:The correct answer is: fraction numerator 1 over denominator 8 x end fraction minus fraction numerator 1 over denominator 4 x to the power of 2 end exponent end fraction plus fraction numerator 1 over denominator 2 x to the power of 3 end exponent end fraction minus fraction numerator 1 over denominator 8 left parenthesis x plus 2 right parenthesis end fraction

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    The partial fractions of fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent over denominator x open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction are

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    fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction then A plus B minus C plus D equals

    fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction then A plus B minus C plus D equals

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    The partial fractions of fraction numerator x to the power of 2 end exponent over denominator open parentheses x to the power of 2 end exponent plus a to the power of 2 end exponent close parentheses open parentheses x to the power of 2 end exponent plus b to the power of 2 end exponent close parentheses end fraction are

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    If fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction then fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals

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    The partial fractions of fraction numerator 6 x to the power of 4 end exponent plus 5 x to the power of 3 end exponent plus x to the power of 2 end exponent plus 5 x plus 2 over denominator 1 plus 5 x plus 6 x to the power of 2 end exponent end fraction are

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    Let a,b,c such that fraction numerator 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 minus 2 x right parenthesis left parenthesis 1 minus 3 x right parenthesis end fraction equals fraction numerator a over denominator 1 minus x end fraction plus fraction numerator b over denominator 1 minus 2 x end fraction plus fraction numerator c over denominator 1 minus 3 x end fraction ,fraction numerator a over denominator 1 end fraction plus fraction numerator b over denominator 3 end fraction plus fraction numerator c over denominator 5 end fraction equals

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    If fraction numerator 2 x plus 1 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent plus 2 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B x plus c over denominator x to the power of 2 end exponent plus 2 end fraction then B=

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