How do you express #(x^2 + 33)/(x^3 + x^2)# in partial fractions? Precalculus Matrix Row Operations Partial Fraction Decomposition (Linear Denominators) 1 Answer Bdub 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)# Answer link Related questions What does partial-fraction decomposition mean? What is the partial-fraction decomposition of #(5x+7)/(x^2+4x-5)#? What is the partial-fraction decomposition of #(x+11)/((x+3)(x-5))#? What is the partial-fraction decomposition of #(x^2+2x+7)/(x(x-1)^2)#? How do you write #2/(x^3-x^2) # as a partial fraction decomposition? How do you write #x^4/(x-1)^3# as a partial fraction decomposition? How do you write #(3x)/((x + 2)(x - 1))# as a partial fraction decomposition? How do you write the partial fraction decomposition of the rational expression #x^2/ (x^2+x+4)#? How do you write the partial fraction decomposition of the rational expression # (3x^2 + 12x -... How do you write the partial fraction decomposition of the rational expression # 1/((x+6)(x^2+3))#? See all questions in Partial Fraction Decomposition (Linear Denominators) Impact of this question 1208 views around the world You can reuse this answer Creative Commons License