Verified answer

(z-8)(z+8)/(z+3) * 1/z(z+8) - (z+8)/z(z-3)= (z-8)/z(z+3) - (z+8)/z(z-3)= ((z-8)*(z-3)-(z+3)(z+8))/z(z+3)(z-3)= (z²-11z+24-z²-11z-24)/z(z+3)(z-3)= -11/z²-9