Can you please help me see what I don't see yet. Here's a problem from a high school textbook (ISBN 978-5-488-02046-7 p.9, #1.029):

$$ \frac{ (a^{1/m}-a^{1/n})^{2} \cdot 4a^{(m+n)/mn} }{ (a^{2/m}-a^{2/n}) (\sqrt[m]{a^{m+1}} + \sqrt[n]{a^{n+1}}) }$$

Here's my try at it: $$\frac{ (a^{1/m} - a^{1/n}) (a^{1/m} - a^{1/n}) \cdot 4 a^{(1/m) + (1/n)} }{ (a^{1/m} - a^{1/n}) (a^{1/m} + a^{1/n}) \cdot a (a^{1/m} + a^{1/n}) }$$

...which is

$$\frac{ (a^{1/m} - a^{1/n}) \cdot 4 a^{(1/m) + (1/n)} }{ a (a^{1/m} + a^{1/n})^2 }$$

Wolfram Alpha's `simplify` stops here, too. I don't see where to go from here. The final form, according to the book, is this:

$$\frac{ 1 }{ a (a^{1/m} - a^{1/n}) }$$

How did they do it?

PS I agree with @You're In My Eye that there's a misprint and instead of multiplication in the numerator there should be an addition sign. I want to express my sincere gratitude to everyone who spent their time to help me. Thank you guys very much.