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Question Number 171999 by Mikenice last updated on 23/Jun/22

resolve: ((4(x−4))/(x^2 −2x−3)) into partial fraction

resolve:4(x−4)x2−2x−3intopartialfraction

Answered by Rasheed.Sindhi last updated on 23/Jun/22

((4(x−4))/((x−3)(x+1)))=(a/(x−3))+(b/(x+1)) 4(x−4)=a(x+1)+b(x−3) x=3: 4(3−4)=4a⇒a=−1 x=−1: 4(−1−4)=−4b⇒b=5 ((4(x−4))/((x−3)(x+1)))=((−1)/(x−3))+(5/(x+1))

4(x−4)(x−3)(x+1)=ax−3+bx+14(x−4)=a(x+1)+b(x−3)x=3:4(3−4)=4a⇒a=−1x=−1:4(−1−4)=−4b⇒b=54(x−4)(x−3)(x+1)=−1x−3+5x+1

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