In the partial fraction decomposition

Question

In the partial fraction decomposition

4x²-35x+34/x³-3x²-10x+24=A/x-2+B/x+3+C/x-4

A=

B=

C=

Answer 1

4x²-35x+34/x³-3x²-10x+24=A/x-2+B/x+3+C/x-4

axl, by formula I sent on previous problem, A=[4*(2²)-(35*2)+34]/(2+3)*(2-4)]=-20/-10=2

B=[4*(-3²)-(35*-3)+34]/(-3-2)*((-3-4)= 175/35=5

C=[4*(4²)-(35*4)+34]/[(4-2)*(4+3)= -42/14= -3

Answer 2

4x² - 35x + 34 = [A(x + 3)(x - 4)] + [B(x - 2)(x + 4)] + [C(x - 2)(x + 3)]

4x² - 35x + 34 = [A(x² - x - 12)] + [B(x² + 2x - 8)] + [C(x² + x - 6)]

4x² - 35x + 34 = Ax² - Ax - 12A + Bx² + 2Bx - 8B + Cx² + Cx - 6C

4x² - 35x + 34 = Ax² + Bx² + Cx² - Ax + 2Bx + Cx - 12A - 8B - 6C

4x² - 35x + 34 = (A + B + C)x² + (-A + 2B + C)x + (-12A - 8B - 6C)

A + B + C = 4

-A + 2B + C = -35

-12A - 8B - 6C = 34

Can you solve for A, B, and C and answer?