<s>[INST] Find the approximate square root of $(a^4-a^{-4})/(a^2-a^{-2})$ Find the approximate square root of
$$\dfrac{\left( \dfrac{12}{5}\right)^4 - \left( \dfrac{5}{12}\right)^4  }{\left( \dfrac{12}{5}\right)^2 - \left( \dfrac{5}{12}\right)^2}$$
I tried using the formula for $(a^4-b^4)$ and $(a^2-b^2)$. Then cancelled the common $(a-b)$, substituted the values and simplified. Didn't work. 
Answer is 13 
Can someone tell me how to solve it with steps of possible? 
It will be a great help 
 [/INST] The fraction itself has a value of around $6$, so the square root of the fraction will be somewhere between $2$ and $3$, and not $13$. How did you get $13$?
The most I was able to simplify the value of the whole expression is that it is equal to $$13^2\left(\frac1{5^2} + \frac1{12^2}\right) - 2$$
Which, I guess, you could say is close to $$\frac{13^2}{5^2} - 2 = \frac{12^2-5^2}{5^2}$$ which is "close" to $\frac{12^2}{5^2}$ and the root of this is $\frac{12}5=2.4$ Which is actually pretty close to the actual answer!
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