Answer
$-\dfrac{9}{40}$
Work Step by Step
Perform the multiplication first to obtain:
\begin{align*}
&=-\frac{9(1)}{4(2)}+\frac{3}{4}\div \frac{5}{6}\\\\
&=-\frac{9}{8} +\frac{3}{4}\div\frac{5}{6}
\end{align*}
Perform the division suing the rule $\dfrac{a}{b} \div \dfrac{c}{d} =\dfrac{a}{b} \times \dfrac{d}{c}$ to obtain"
\begin{align*}
\require{cancel}
&=-\frac{9}{8} + \frac{3}{4}\times \frac{6}{5}\\\\
&=-\frac{9}{8} + \frac{3}{\cancel{4}2}\times \frac{\cancel{6}3}{5}\\\\
&=-\frac{9}{8} + \frac{3(3)}{2(5)}\\\\
&=-\frac{9}{8} + \frac{9}{10}\\\\
\end{align*}
Make the fractions similar using their LCD of $40$ then add to obtain:
\begin{align*}
&=-\frac{9(5)}{8(5)} + \frac{9(4)}{10(4)}\\\\
&=-\frac{45}{40}+\frac{36}{40}\\\\
&=\frac{-45+36}{40}\\\\
&=-\frac{9}{40}
\end{align*}
