Simplifying a radical with fraction and sum What are the steps to simplify
$(1+(\frac{1}{2}(x^3-\frac{1}{x^3})^2))^ \frac{1}{2}$
to
$\frac{1}{2}(x^3+\frac{1}{x^3})$ ?

If what you have is $$ \sqrt{ 1 + \frac{1}{2}(x^3 - \frac{1}{x^3})^2} $$
$$ \sqrt{ 1 + \frac{(x^6 - 1)^2}{2x^6}} = \sqrt{ \frac{x^{12 } + 1}{2x^6}} = \sqrt{ \frac{1}{2}(x^6 + \frac{1}{x^6})}$$
So they are not equal.
