Find the real and imaginary part of the following I'm having trouble finding the real and imaginary part of $z/(z+1)$ given that z=x+iy.  I tried substituting that in but its seems to get really complicated and I'm not so sure how to reduce it down.  Can anyone give me some advice?

Just multiply the fraction by the complex conjugate of $z+1$, that is,
\begin{equation*}
\frac{z}{z+1} = \frac{x+iy}{1+x+iy} = \frac{1+x-iy}{1+x-iy} \frac{x+iy}{1+x+iy} = \frac{(1+x)x+y^2+iy }{(1+x)^2+y^2} =
\end{equation*}
\begin{equation*}
= \frac{(1+x)x+y^2}{(1+x)^2+y^2} + i \frac{y}{(1+x)^2+y^2}
\end{equation*}
