Enter (A,B,C) in order below if A, B, and C are the coefficients of the partial fractions expansion of (2x^2 + 3x - 5)/(x(x^2 - 1)) = A/x + B/(x - 1) + C/(x + 1).
+128475 Note that x (x^2 -1) = (x)(x + 1) ( x - 1)
Multiply throght by ths factorization and we have
2x^2 + 3x - 5 = A ( x - 1)(x + 1) + B(x)(x + 1) + C(x)(x - 1) simplify
2x^2 + 3x -5 = A ( x^2 -1) + B( x^2 + x) + C(x^2 - x)
2x^2 + 3x - 5 = (A + B + C)x^2 + (B - C)x - A
Equating terms we have this syatem
A + B + C = 2
B - C = 3 (1)
A = 5
So
5 + B + C = 2
B + C = -3 (2)
Adding (1) and (2) we get that 2B = 0 so B = 0
So
5 + 0 + C =2
C = 2 -5 = -3
(A,B,C) = (5, 0 , -3)
