For the function $f(x)=x$ where x belongs to [0,$\pi$], I have found the Fourier series for $f_e(x)$ and $f_o(x)$.
If I wanted to find the Fourier Series of the function, can I add the series together, if not is there a shortcut method to calculate the Fourier series for $f(x)=x$?
Yes you can add the even and odd Fourier series. This is because breaking the series into real-valued even and odd series is a special case of the more general complex Fourier series where you treat $e^{ix}$ as separate cosine and sine terms with real coefficients.