Consider the steady, two$-$dimensional velocity field given by

$v_1=1+\frac{x_2^2-x_1^2}{(x_1^2+x_2^2{)}^2},v_2=-\frac{2x_1{x}_2}{(x_1^2+x_2^2{)}^2}$

Find the velocity gradient tensor $L,$ the deformation tensor $D,$ the vorticity vector $,$ the expansion rate

var$,$ and the invariants of $L$ and $D.$