How to sum functions and get an expression in order to a given variable?

For example, if a have:

    x=@(t) 1+ t + 3t^2 + 5t^3 + 9t^4;
    y=@(t) 1+ t + 3t^2
    z=@(t) x(t)-y(t)

can i get an answer like:

    x(t)-y(t)= 5t^3 + 9t^4

Answer 1

[John D'Errico]

Why would you think it possible or not? Did you try it?

x=@(t) 1+ t + 3*t^2 + 5*t^3 + 9*t^4;
y=@(t) 1+ t + 3*t^2;
z=@(t) x(t)-y(t)

syms t
z(t)
ans =
  9*t^4 + 5*t^3

If your question is can you actually get something like this:

x(t)-y(t) = 5t^3 + 9t^4

I'm not really sure what you mean by that, or what is your goal.