[fdymendo]

 no he podido hacer nada 

\( \displaystyle\frac{( a + \displaystyle\frac{1}{b})^m ( a - \displaystyle\frac{1}{b})^n}{( b + \displaystyle\frac{1}{a})^m ( b - \displaystyle\frac{1}{a})^n} \)

[Abdulai]

Notar que:   \( \left(a+\frac{1}{b}\right)^n=\dfrac{(ab+1)^n}{b^n} \)