9514 1404 393
Answer:
(A, B, C) = (-1, 2, 2)
Explanation:
Simplify the right side and equate coefficients of the x-terms.
x² -3 = A(x² +1) +(Bx +C)(x -1)
x² -3 = Ax² +A +Bx² -Bx +Cx -C
x² -3 = (A+B)x² +(C-B)x +(A-C) . . . . identify coefficients of each x-term
Matching coefficients on the left and right gives rise to three equations in the three unknowns:
A +B = 1
C -B = 0
A -C = -3
Adding all three equations, we get ...
(A +B) +(C -B) +(A -C) = (1) +(0) +(-3)
2A = -2
A = -1 . . . . . . divide by 2
B = 1 -A = 2
C = B = 2
The coefficients are ...
(A, B, C) = (-1, 2, 2)