To find the growth rate of the total exports \(X\), we need to understand the individual growth contributions from goods and services exports.

1. Given the exports of goods, \(G = G(t)\), the growth rate is \(\frac{a}{t}\). This implies that the rate of change of goods exports with respect to time is proportional to \(\frac{a}{t}G\).
2. For exports of services, \(S = S(t)\), the growth rate is \(\frac{b}{t}\). Similarly, the rate of change of services exports is proportional to \(\frac{b}{t}S\).
3. The total exports \(X = G + S\). We seek the growth rate of \(X\).
4. The rate of change of total exports, \(\frac{dX}{dt}\), is the sum of the rates of change of \(G\) and \(S\), which is: \(\frac{dG}{dt} + \frac{dS}{dt} = \frac{a}{t}G + \frac{b}{t}S\).
5. The growth rate of total exports \(X\) with respect to time \(t\) is: \[ \frac{\frac{dX}{dt}}{X} = \frac{\frac{a}{t}G + \frac{b}{t}S}{G + S} = \frac{Ga + Sb}{tX} \]

This corresponds to the option \((Ga + Sb)/(tX)\). Hence, this is the correct answer.

Let's eliminate the other options for clarity:

• \(\frac{a}{t} + \frac{b}{t}\) assumes direct addition of growth rates but ignores the relative contributions of goods and services, which is not correct.
• \(\frac{a}{G} + \frac{b}{S}\) is incorrect as it suggests an inverse relationship not pertaining to the growth rate concept described.
• \(\frac{(a+b)}{(G+S)}\) simplifies both \(a\) and \(b\) into a single fraction, ignoring the individual influence proportional to \(G\) and \(S\).