How to get 1 as the highest order coefficient in a polynomial expression?

Hi,

I would like to get 1 as the highest order coefficient in the denomitor. How can I get that?

clear; clc

syms p K_s0 Phi_V Phi_G s K_p K_x0 T_i real;

Phi_V = -p*(K_p/K_x0)*(1 + 1/(s*T_i))*1/s;

eqn1 = p == K_s0*(Phi_V + Phi_G);

eqn2 = isolate(eqn1, p);

eqn3 = collect(eqn2/Phi_G, s); disp(char(eqn3))

p/Phi_G == ((K_s0*K_x0*T_i)*s^2)/((K_x0*T_i)*s^2 + (K_p*K_s0*T_i)*s + K_p*K_s0)

[Torsten]

According to which variable is 1 the highest coefficient in the denominator ?

[John D'Errico]

Are you looking to find a partial fraction decomposition of the function?

Answer 1

[Walter Roberson]

syms p K_s0 Phi_V Phi_G s K_p K_x0 T_i real;
Phi_V = -p*(K_p/K_x0)*(1 + 1/(s*T_i))*1/s;
eqn1 = p == K_s0*(Phi_V + Phi_G);
eqn2 = isolate(eqn1, p);
eqn3 = collect(eqn2/Phi_G, s); disp(char(eqn3))

p/Phi_G == ((K_s0*K_x0*T_i)*s^2)/((K_x0*T_i)*s^2 + (K_p*K_s0*T_i)*s + K_p*K_s0)

[N,D] = numden(rhs(eqn3))
c = coeffs(D,s,'all');
N1 = N/c(1)
D1 = expand(D/c(1))
eqn4 = lhs(eqn3) == N1/D1; disp(char(eqn4))

p/Phi_G == (K_s0*s^2)/(s^2 + (K_p*K_s0*s)/K_x0 + (K_p*K_s0)/(K_x0*T_i))