Answer
$-\dfrac{2}{5}$
Work Step by Step
Perform division first:
\begin{align*}
\require{cancel}
&=\frac{1}{2} - \left(\frac{2}{3} \times \frac{9}{5}\right) +\frac{3}{10}\\\\
&=\frac{1}{2} - \left(\frac{2}{\cancel{3}} \times \frac{\cancel{9}3}{5}\right) +\frac{3}{10}\\\\
&=\frac{1}{2} - \frac{6}{5} +\frac{3}{10}\\\\
\end{align*}
Make the fractions similar using their LCD which is $10$ to obtain:
\begin{align*}
&=\frac{5}{10}-\frac{12}{10}+\frac{3}{10}
\end{align*}
Perform the subtraction first (since it comes first from the left) then addition next to obtain:
\begin{align*}
&=\frac{5-12}{10}+\frac{3}{10}\\\\
&=\frac{-7}{10}+\frac{3}{10}\\\\
&=-\frac{4}{10}\\\\
&=-\frac{2}{5}
\end{align*}
