How do you express #1/(e^x(e^x+1))# in partial fractions? Precalculus Matrix Row Operations Partial Fraction Decomposition (Linear Denominators) 1 Answer Cesareo R. Jun 11, 2016 #1/(e^x(e^x+1)) = 1/e^x-1/(e^x+1)# Explanation: Making #1/(e^x(e^x+1)) = A/e^x+B/(e^x+1)# after equating numerator coefficients we have #{ (A+B=0), (A=1) :}# Solving for #A,B# we obtain #1/(e^x(e^x+1)) = 1/e^x-1/(e^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 2023 views around the world You can reuse this answer Creative Commons License