Question 20736
Ok, first you need to solve the quadratic.  It doesn't factor so use the quadratic formula: {{{x=(-b+-sqrt(b^2-4ac))/2a}}}

{{{x=(-3+-sqrt(9-32))/8}}}
{{{x=(-3+-sqrt(-23))/8}}}

The roots are:
{{{A = -3/8 + (1/8)sqrt(23)i}}}
{{{B = -3/8 - (1/8)sqrt(23)i}}}

To find {{{1/A + 1/B}}} first simplify to: {{{(A+B)/AB}}}

{{{A+B = (-3/8 + (1/8)sqrt(23)i) + (-3/8 - (1/8)sqrt(23)i)}}} = {{{-6/8 = -3/4}}}
{{{AB = (-3/8 + (1/8)sqrt(23)i)(-3/8 - (1/8)sqrt(23)i)}}} = {{{9/64 - (1/64)(23)i^2}}} + {{{9/64 + 23/64 = 32/64}}} = {{{1/2}}}

Finally, {{{(A+B)/AB = (-3/4)/(1/2)}}} = {{{(-3/4)(2) = -3/2}}}