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

1 Answer

Mar 8, 2016

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

Explanation:

#(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)#

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