The form of the partial fraction decomposition of a rational function is given. (2𝑥^2+4𝑥+26)/[(𝑥+2)(𝑥^2+9)]=𝐴/(𝑥+2)+(𝐵𝑥+𝐶)/(𝑥^2+9)

Question

determine what A, B and C are equal to

Answer 1

2x² + 4x + 26 = A(x² + 9) + B(x + 2) + C

2x² + 4x + 26 = Ax² + 9A + Bx + 2B + C

A = 2

B = 4

C = 0

[2 / (x + 2) + [4 / (x² + 9)]