It is likely easiest to define a third variable, then set that equal to what you want:
function [n] = n(x,y)
z = x+y+1;
syms q
n = (q^(z/2)-q^(-z/2))/(q^(1/2)-q^(-1/2))
end
For:
x = 3;
y = 10;
the result is:
n =
(1/q^7 - q^7)/(1/q^(1/2) - q^(1/2))
.