How do you express #((x^3+1)/(x^2+3))# in partial fractions? Precalculus Matrix Row Operations Partial Fraction Decomposition (Linear Denominators) 1 Answer Shwetank Mauria Feb 15, 2017 #(x^3+1)/(x^2+3)=x-(3x-1)/(x^2+3)# Explanation: #x^3+1=x(x^2+3)-3x+1# Hence, #(x^3+1)/(x^2+3)=x+(-3x+1)/(x^2+3)# or #x-(3x-1)/(x^2+3)# As #x^2+3# cannot be factorized, you cannot have further partial fractions. 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 1115 views around the world You can reuse this answer Creative Commons License