Expected Value of the Ratio of Independent Variables, E(X/(X+Y))

Question

If $X$ and $Y$ are independent random variables, is the following true? Is there an easy way to show this?

$$E\left[\frac{X}{X+Y}\right]=\frac{E[X]}{E[{X+Y}]}=\frac{E[X]}{E[X]+E[Y]}$$

If this is not true in general, are there special cases when it is true (e.g. what $X$ and $Y$ are strictly positive and finite)?

Thanks for the help!