Answer
$\dfrac{\dfrac{1}{2}+\dfrac{2}{3}}{\dfrac{5}{9}-\dfrac{5}{6}}=-\dfrac{21}{5}$
Work Step by Step
$\dfrac{\dfrac{1}{2}+\dfrac{2}{3}}{\dfrac{5}{9}-\dfrac{5}{6}}$
Evaluate the sum in the numerator and the substraction in the denominator:
$\dfrac{\dfrac{1}{2}+\dfrac{2}{3}}{\dfrac{5}{9}-\dfrac{5}{6}}=\dfrac{\Big(\dfrac{3+4}{6}\Big)}{\Big(\dfrac{30-45}{54}\Big)}=\dfrac{\dfrac{7}{6}}{\dfrac{-15}{54}}=...$
Evaluate the division and simplify:
$...=\dfrac{7}{6}\div\dfrac{-15}{54}=\dfrac{(7)(54)}{-(15)(6)}=-\dfrac{378}{90}=-\dfrac{21}{5}$