Find the Partial Fraction Decompostion for -13x-37/x4-x3+x2-3x-6
factoring x^4 - x^3 + x^2 - 3x - 6
= ( x + 1 ) ( x- 2) (x^2 + 3)
so, we can write
( - 13x - 37 ) / ( x + 1 ) ( x- 2) (x^2 + 3) = ao / ( x+ 1) + a1 / ( x - 2) + ( a3x + a2 ) / ( x^2 + 3)
( - 13x - 37 ) / ( x + 1 ) ( x- 2) (x^2 + 3) = ao ( x - 2) ( x^2 + 3) + a1 ( x +1) ( x^2 + 3) + ( a3x + a2 ) ( x+ 1 )( x - 2) / ( x + 1 ) ( x- 2) (x^2 + 3)
a0 = 1 , a 1 = - 3
a3 = 1 , a2 = 8
hence, partial fraction decomposition is
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