Answer
a) $(\dfrac{2}{x+2y}-\dfrac{3}{x+3z})i+(\dfrac{3}{2y+3z}-\dfrac{1}{x+2y})j+(\dfrac{1}{x+3z}-\dfrac{2}{2y+3z})k$
b) $0$
Work Step by Step
a) Consider $F=A i+B j+C k$
Then $curl F=\begin{vmatrix}i&j&k\\\dfrac{\partial}{\partial x}&\dfrac{\partial }{\partial y}&\dfrac{\partial }{\partial z}\\A&B&C\end{vmatrix}$
$curl F=[C_y-B_z]i+[A_z-C_z]j+[B_x-A_y]k$
$curl F=(\dfrac{2}{x+2y}-\dfrac{3}{x+3z})i+(\dfrac{3}{2y+3z}-\dfrac{1}{x+2y})j+(\dfrac{1}{x+3z}-\dfrac{2}{2y+3z})k$
b) $div F=\dfrac{\partial A}{\partial x}+\dfrac{\partial B}{\partial y}+\dfrac{\partial C}{\partial z}$
$div F=\dfrac{\partial [\ln (2y+3z)]}{\partial x}+\dfrac{\partial [\ln (x+3z)]}{\partial y}+\dfrac{\partial [\ln (x+2y)]}{\partial z}=0$
