Find constants A and B such that
x+7x2−x−2=Ax−2+Bx+1
for all x such that x does not equal -1 and x does not equal 2. Give your answer as the ordered pair.
Your answer is better than mine Alan. it is better explained.
I rarely touch questions that are presented so poorly. Maybe that is why Lightning reposted.
Or maybe this question was posted by someone else in his class.
Ref for others : https://web2.0calc.com/questions/help_51906
Multiplying both sides by $(x - 2)(x + 1) = x^2 - x - 2$, we get x+7=A(x+1)+B(x−2)=Ax+Bx+A−2B=(A+B)x+(A−2B). Comparing the coefficients on both sides, we obtain the system of equations A+B=1,A−2B=7. Subtracting the second equation from the first equation, we get $3B = 1 - 7 = -6$, so $B = -2$. Then from the first equation, $A = 1 - B = 3$. Hence, x+7x2−x−2=3x−2−2x+1, and our answer is (A,B)=(3,−2).