## College Algebra 7th Edition

$\displaystyle -\frac{3}{2}\pm\frac{\sqrt{3}}{2}i$
First we multiply through by $t$: $t+3+\displaystyle \frac{3}{t}=0$ $t^{2}+3t+3=0$ Next we use the quadratic formula ($a=1, b=3, c=3$): $\displaystyle t=\frac{-3\pm\sqrt{(3)^{2}-4*1*3}}{2(1)}=\frac{-3\pm\sqrt{9-12}}{2}=\frac{-3\pm\sqrt{-3}}{2}=\frac{-3\pm \sqrt{3}i}{2}=-\frac{3}{2}\pm\frac{\sqrt{3}}{2}i$