How do you express #(3x )/ (x^2 * (x^2+1) )# in partial fractions? Precalculus Matrix Row Operations Partial Fraction Decomposition (Linear Denominators) 1 Answer Shwetank Mauria May 8, 2016 #(3x)/(x^2*(x^2+1))=3/x-(3x)/(x^2+1)# Explanation: #(3x)/(x^2*(x^2+1))=3/(x*(x^2+1)# and let its partial fractions be #3/(x*(x^2+1))hArrA/x+(Bx+C)/(x^2+1)# or #3/(x*(x^2+1))hArr(A(x^2+1)+x(Bx+C))/(x*(x^2+1))# or #3/(x*(x^2+1))hArr(x^2(A+B)+Cx+A)/(x*(x^2+1))# or #A+B=0#, #C=0# and #A=3#. Thus #B=-3# Hence #(3x)/(x^2*(x^2+1))=3/x-(3x)/(x^2+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 1830 views around the world You can reuse this answer Creative Commons License