How do you express $(x^2 + 33)/(x^3 + x^2)$ in partial fractions?

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Answer 1 · 2016-03-08T18:13:01

$(x^2+33)/(x^2(x+1)) = -33/x +33/x^2 +34/(x+1)$

$(x^2+33)/(x^2(x+1)) = A/x +B/x^2 +C/(x+1)$

$x^2+33 = A(x(x+1))+B(x+1)+Cx^2$

$x^2+33 = Ax^2+Ax+Bx+B+Cx^2$

$1=A+C, 0=A+B, 33=B$

$A=-33, B=33, C=34$

$(x^2+33)/(x^2(x+1)) = -33/x +33/x^2 +34/(x+1)$

How do you express (x^2 + 33)/(x^3 + x^2)(x^2 + 33)/(x^3 + x^2) in partial fractions?