> restart;

> eq1:=diff((rho/(rho^2+z^2)^(1/2))^n,rho)+diff((z/(rho^2+z^2)^(1/2))^n,z)+((rho/(rho^2+z^2)^(1/2))^n)/rho;

eq1 := (rho/(rho^2+z^2)^(1/2))^n*n*(1/(rho^2+z^2)^(1/2)-rho^2/(rho^2+z^2)^(3/2))*(rho^2+z^2)^(1/2)/rho+(z/(rho^2+z^2)^(1/2))^n*n*(1/(rho^2+z^2)^(1/2)-z^2/(rho^2+z^2)^(3/2))*(rho^2+z^2)^(1/2)/z+(rho/(r...

> simplify(%);

((rho/(rho^2+z^2)^(1/2))^n*n*z^3+(z/(rho^2+z^2)^(1/2))^n*n*rho^3+(rho/(rho^2+z^2)^(1/2))^n*z*rho^2+(rho/(rho^2+z^2)^(1/2))^n*z^3)/((rho^2+z^2)*rho*z)

> factor(%);

((rho/(rho^2+z^2)^(1/2))^n*n*z^3+(z/(rho^2+z^2)^(1/2))^n*n*rho^3+(rho/(rho^2+z^2)^(1/2))^n*z*rho^2+(rho/(rho^2+z^2)^(1/2))^n*z^3)/((rho^2+z^2)*rho*z)

> eq2:=diff(1-(rho/(rho^2+z^2)^(1/2))^n,rho)+diff(1-(z/(rho^2+z^2)^(1/2))^n,z)+(1-(rho/(rho^2+z^2)^(1/2))^n)/rho;

eq2 := -(rho/(rho^2+z^2)^(1/2))^n*n*(1/(rho^2+z^2)^(1/2)-rho^2/(rho^2+z^2)^(3/2))*(rho^2+z^2)^(1/2)/rho-(z/(rho^2+z^2)^(1/2))^n*n*(1/(rho^2+z^2)^(1/2)-z^2/(rho^2+z^2)^(3/2))*(rho^2+z^2)^(1/2)/z+(1-(rh...

> simplify(%);

-((rho/(rho^2+z^2)^(1/2))^n*n*z^3+(z/(rho^2+z^2)^(1/2))^n*n*rho^3-z*rho^2-z^3+(rho/(rho^2+z^2)^(1/2))^n*z*rho^2+(rho/(rho^2+z^2)^(1/2))^n*z^3)/((rho^2+z^2)*rho*z)

>