Help with simplification of a rational expression (with fractional powers) 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.

After checking the older edition of the book, I'm quite sure that the original problem looked like this:

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

Now we have:
$$(a^{1/m}-a^{1/n})^{2} \color{blue}{+} 4a^{(m+n)/mn} =(a^{1/m}+a^{1/n})^{2}$$
$$(a^{2/m}-a^{2/n}) (\sqrt[m]{a^{m+1}} + \sqrt[n]{a^{n+1}})=a(a^{1/m}-a^{1/n})^{2}(a^{1/m}+a^{1/n})^2$$
Finally we get:
$$\frac{ (a^{1/m}-a^{1/n})^{2} \color{blue}{+} 4a^{(m+n)/mn} }{ (a^{2/m}-a^{2/n}) (\sqrt[m]{a^{m+1}} + \sqrt[n]{a^{n+1}}) }=\frac{1}{a(a^{1/m}-a^{1/n})}$$
