The expression in the image appears to be:

$\frac{\frac{a^{\frac{1}{2}} + ab^{-1}}{\frac{a^{\frac{1}{3}} - a^{\frac{1}{2}} b^{\frac{1}{3}} + b^{-\frac{2}{3}}}{}} - \frac{a}{\sqrt[3]{b}}}{}$

Would you like a step-by-step solution or details on simplifying this expression?

Here are 5 follow-up questions that might deepen your understanding:

1. How does changing the exponents affect the overall expression?
2. Can this expression be simplified by factoring?
3. How does rationalizing the denominators impact the result?
4. What does each term represent if you consider $a$ and $b$ as specific values?
5. How does fractional exponent notation relate to radical notation?

Tip: Remember that $b^{-1}$ is equivalent to $\frac{1}{b}$, which can simplify calculations.