Find constants A and B such that (x + 7)/(x^2 - x - 2) = A/(x - 2) + B/(x + 1) for all x such that x ≠ 1 and x ≠ 2. Give your answer as the ordered pair (A,B).
If you guys are able to solve this quickly then that would be great!
This is known as finding the partial fraction expansionx+7x2−x−2=x+y(x−2)(x+1)=Ax−2+Bx−1
x+7(x−2)(x+1)=A(x+1)+B(x−2)(x−2)(x+1)∀x:x≠2, −1x+7=A(x+1)+B(x−2)x=(A+B)x⇒1=A+B7=A−2B
B=1−A7=A−2(1−A)=3A−23A=9A=3B=1−3=−2x+7(x−2)(x+1)=3x−2−2x+1
