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Question Number 209129 by Adeyemi889 last updated on 02/Jul/24

Answered by A5T last updated on 02/Jul/24

((x^3 +3)/(x^2 −1))=((x(x^2 −1)+x+3)/(x^2 −1))=x+((x+3)/(x^2 −1)) ((x+3)/(x^2 −1))=(A/(x−1))+(B/(x+1))⇒x+3=(A+B)x+A−B ⇒A+B=1;A−B=3⇒A=2;B=−1 ⇒((x^2 +3)/(x^2 −1))=x+(2/(x−1))−(1/(x+1))

x3+3x2−1=x(x2−1)+x+3x2−1=x+x+3x2−1x+3x2−1=Ax−1+Bx+1⇒x+3=(A+B)x+A−B⇒A+B=1;A−B=3⇒A=2;B=−1⇒x2+3x2−1=x+2x−1−1x+1

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