How to add compound fractions? How to add two compound fractions with fractions in numerator like this one:
$$\frac{\ \frac{1}{x}\ }{2} + \frac{\ \frac{2}{3x}\ }{x}$$
or fractions with fractions in denominator like this one:
$$\frac{x}{\ \frac{2}{x}\ } + \frac{\ \frac{1}{x}\ }{x}$$

Yet another strategy:
\begin{align}
\frac{\frac1x}2+\frac{\frac2{3x}}x&=\frac1{2x}+\frac2{3x^2}\\
&=\frac{3x}{6x^2}+\frac4{6x^2}=\frac{3x+4}{6x^2}\,.
\end{align}
What did I do? Given is the sum of two fractions, and I multiplied top-and-bottom of the first by $x$, and top-and-bottom of the second by $3x$. Second step, find the minimal common denominator, which is $6x^2$, and on each of your current fractions, multiply top-and-bottom by a suitable quantity to get the denominators equal. Now add.
