Am really not sure how to prove this question, does
= (\frac{1}{x^{2}+y^{2}+z^{2})^{1/2} ( x+y+z) [/tex]
$\dfrac {\vec{r}} {\| \vec{r} \|} = \left\{ \dfrac {x} {\sqrt{x^2+y^2+z^2}},\dfrac {y} {\sqrt{x^2+y^2+z^2}},\dfrac {z} {\sqrt{x^2+y^2+z^2}} \right \}$
Take the divergence and then take the gradient and plow through the algebra. It's not that bad. You end up with the right hand side when you're done.
if you move the delx operator inside those braces, then what you have there is the div operator. Once you find that you'll have a scalar function in 3 variables, (x, y, z). Take the gradient of that function, simplify it, substitute r in where appropriate and you'll end up with the answer.