Solving equations for Variable/Variable

I have a simple question but i have not been able to find a way to achive this and was looking for some help. For example if I have the following code

syms A B C D E
eqn = (A*B*C)/E == D;

Is it there a function that will allow me to solve for C/D = ?. I have tried using solve but this provides a struct variable that solve the equation for c and D aka (solves for C= and D=).

Thanks

Answer 1

[John D'Errico]

No reason you cannot do this:

syms A B C D E
eqn = (A*B*C)/E == D;

syms CoverD
solve(subs(eqn,C,CoverD*D),CoverD)

ans = 

[Isaac Kambouris]

Thanks for the help. I am not really sure why this solution works could you elaberate on how using the CoverD makes the solution work?

[John D'Errico]

Just look. Take it apart.

syms A B C D E
eqn = (A*B*C)/E == D;
syms CoverD;

Effectively, I define the variable CoverD as C/D. So if we accept that

CoverD = C/D

then multiply by D. Can you solve for C? I hope so.

So what does this substitution do?

subs(eqn,C,CoverD*D)

ans = 

It replaces C with the product CoverD*D. Now what happens to D in that expression? It effectively goes away, as long as D is not zero. And if D was zero, then what would be the meaning of the ratio C/D anyway? So we can assume D is never zero in this context.

The final solve should now be clear.

[Isaac Kambouris]

Ah thank you that makes a lot sense