Logical False before subs then Logical True?

I am trying to verify if 2 equations are symbolically equivalent. I did a logical check and it return false. When I solve these equations in terms of S/K by using a variable substitution, i.e. Z=S/K -> K=S*K, the logical is true. I can't seem to figure out why this is so.

syms S K r_x Z D 

Solution=solve(0 == -S*(r_x)^2 + 2*(K+S)*r_x -S,r_x )

Expanded_Solution=expand(Solution(2,1))

%Sections=children(Expanded_Solution)

D=1 + (K/S) - sqrt( (1+(K/S))^2 -1)

Boolen_check_1=logical(D == Expanded_Solution)

% Z=K/S --> K = Z*S 

new_1=subs(Expanded_Solution,K, (Z*S) ) 
new_2=subs(D,K, (Z*S))

trial_1=solve(new_1 - r_x == 0, Z)

trial_2=solve(new_2 - r_x == 0, Z)

Boolen_check_2 = logical(trial_1 == trial_2)

Answer 1

[madhan ravi]

You can’t prove two symbolic equations which are in different form that are equal (matlab won’t recognise), the last thing which you did by substituting is the appropriate way

simple try :

fplot(subs(Expanded_Solution,K,2 ))
hold on
fplot(subs(D,K,2))

and see the difference between the graph when you change the form of an equation the behaviour is totally different

Always use isequaln()(link) to compare symbolic equations.

[Adam Watts]

Can you expand on why one can't prove two symbolic equations which are in different forms are equal and why substitution worked?

Answer 2

[Steven Lord]

Use isAlways.

isAlways(trial_1 == trial_2)

[Adam Watts]

I tried this and nothing changed, still returns a true while the statement above gets a false.