Answer
$-1\frac{1}{36}$
Work Step by Step
Simplify the complex fraction to obtain:
\begin{align*}
\require{cancel}
&=\frac{\frac{7}{9}-\frac{27}{9}}{\frac{5}{6}}\div \frac{3}{2}+\frac{3}{4}\\\\
&=\frac{\frac{7-27}{9}}{\frac{5}{6}}\div \frac{3}{2}+\frac{3}{4}\\\\
&=\frac{\frac{-20}{9}}{\frac{5}{6}}\div \frac{3}{2}+\frac{3}{4}\\\\
&=\left(\frac{-20}{9} \times \frac{6}{5}\right)\div \frac{3}{2}+\frac{3}{4}\\\\
&=\left(\frac{-\cancel{20}4}{\cancel{9}3} \times \frac{\cancel{6}2}{\cancel{5}}\right)\div \frac{3}{2}+\frac{3}{4}\\\\
&=\frac{-4(2)}{3}\div \frac{3}{2}+\frac{3}{4}\\\\
&=\frac{-8}{3}\div \frac{3}{2}+\frac{3}{4}\\\\
\end{align*}
Perform the division using the rule $\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}$ to obtain:
\begin{align*}
&=\frac{-8}{3} \times \frac{2}{3}+\frac{3}{4}\\\\
&=\frac{-8(2)}{3(3)}+\frac{3}{4}\\\\
&=\frac{-16}{9}+\frac{3}{4}\\\\
&=\frac{-16(4)}{9(4)}+\frac{3(9)}{4(9)}\\\\
&=\frac{-64}{36}+\frac{27}{36}\\\\
&=\frac{-64+27}{36}\\\\
&=-\frac{37}{36}\\\\
&=-1\frac{1}{36}
\end{align*}
