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 

Let $x= \frac{12}{5}$ to obtain
\begin{align}
f(x) &= \frac{x^{4} + \frac{1}{x^{4}}}{x^{2} + \frac{1}{x^{2}}} = \frac{x^{8}-1}{x^{2} \, (x^{4}-1)} = \frac{x^{4} + 1}{x^{2}} = x^{2} + \frac{1}{x^{2}} = \left(x + \frac{1}{x}\right)^{2} - 2 
\end{align}
Taking the square root of both sides leads to
\begin{align}
\sqrt{f(x)} = \sqrt{x^{2}+ \frac{1}{x^{2}}} = x \, \sqrt{1 + \frac{1}{x^{4}}} = x \, \left( 1 + \frac{1}{2 \, x^{4}} - \frac{1}{8 \, x^{8}} + \mathcal{O}\left(\frac{1}{x^{10}}\right) \right) \approx x
\end{align}
