Apply partial traction to the equation Vx s 15 times3 50 x

Apply partial traction to the equation V_x (s) = 15 times^3 + 50 x^2 + 160 x/(x^2 + 4)(x^2 + 2.5 x 5)

V_x(s) = (Ax+D)/(x²+4) +(Bx+C)/(x² +5x/2 +5)

Ax³ + 5AX²/2 +5Ax +Dx²+5Dx/2 +5D +Bx³+Cx²+ 4Bx +4C = 15x³ +50x² +160x

(A+B)x³ +(5A/2+C+D)x² + (5A+5D/2+4B)x +4C +5D= 15x³ +50x² +160x

A+B = 15 ; 4C+5D = 0; 5A/2+C+D = 50; 5A+5D/2 +4B = 160

A = 15-B and C = -5D/4

5A/2 +C +D = (75-5B)/2 -5D/4 + D = 50

-D/4 -5B/2 = 12.5 ; 10B +D = -50 ----------------1

and

5(15-B)+5D/2 +4B = 160

5D/2 -B = 85

5D -2B =170 -------------------2

using eqn 1 in eqn 2:

5(-50-10B) -2B =170

-250 -52B = 170

-52B = 420

B = -8.079 ; A = 23.079 ;D = 30.79;C = -38.49