When a question gives α+β and αβ, try to rewrite the required expression using only these two quantities. For reciprocals, use 1/α + 1/β = (α+β)/(αβ), because the common denominator is αβ. Here, 1/α+1/β=(α+β)/(αβ). Therefore the value is -8/-9=8/9. Notice that this method avoids finding α and β separately.