How do you express # (x^2+x+1)/(1-x^2)# in partial fractions? Precalculus Matrix Row Operations Partial Fraction Decomposition (Irreducible Quadratic Denominators) 1 Answer Shwetank Mauria May 8, 2016 #(x^2+x+1)/(1-x^2)=-1+3/(2(1-x))+1/(2(1+x))# Explanation: #(x^2+x+1)/(1-x^2)=-1+(1-x^2+x^2+x+1)/(1-x^2)# or #(x^2+x+1)/(1-x^2)=-1+(x+2)/(1-x^2)# and let #(x+2)/(1-x^2)=(x+2)/((1-x)(1+x))hArrA/(1-x)+B/(1+x)# or #(x+2)/((1-x)(1+x))hArr(A(1+x)+B(1-x))/((1-x)(1+x))# or #(x+2)/((1-x)(1+x))hArr((A-B)x+(A+B))/((1-x)(1+x))# or Hence #A-B=1# and #A+B=2# or #A=3/2# and #B=1/2# Hence #(x^2+x+1)/(1-x^2)=-1+3/(2(1-x))+1/(2(1+x))# Answer link Related questions How do I find the partial-fraction decomposition of #(3x^2+2x-1)/((x+5)(x^2+1))#? How do I find the partial-fraction decomposition of #(s+3)/((s+5)(s^2+4s+5))#? How do I find the partial-fraction decomposition of #(x^4 + 5x^3 + 16x^2 + 26x + 22)/(x^3 + 3x^2... How do I find the partial-fraction decomposition of #(-3x^3 + 8x^2 - 4x + 5)/(-x^4 + 3x^3 - 3x^2... How do I find the partial-fraction decomposition of #(2x^3+7x^2-2x+6)/(x^4+4)#? What is meant by an irreducible quadratic denominator? How do irreducible quadratic denominators complicate partial-fraction decomposition? How do I decompose the rational expression #(x-3)/(x^3+3x)# into partial fractions? How do I decompose the rational expression #(x^5-2x^4+x^3+x+5)/(x^3-2x^2+x-2)# into partial fractions? How do I decompose the rational expression #(-x^2+9x+9)/((x-5)(x^2+4))# into partial fractions? See all questions in Partial Fraction Decomposition (Irreducible Quadratic Denominators) Impact of this question 1753 views around the world You can reuse this answer Creative Commons License