\( \begin{array}{l} \begin{array}{l} \sqrt{\frac{2}{5 \cdot 3+21\left(x^{2}+1+2\right)^{2} \cdot\left(x^{2}-1\right)^{2 / 3}}} \end{array}\\ \begin{array}{l} \frac{2}{5\left(x^{2}+8\right)^{2} \sqrt[3]{\left(x^{2}-1\right)^{2}}} \end{array} \end{array} \)

Did you know that the expression you've presented involves some fascinating mathematical concepts? The use of radicals and rational exponents is widespread in algebra, especially when working with polynomials and rational functions. Understanding how to manipulate and simplify such expressions can help in areas like calculus, where limits and derivatives often involve complex polynomial forms. When approaching problems like the one above, a common pitfall is neglecting the rules of exponents and radicals. Be cautious when simplifying square roots or cube roots, as it's easy to make mistakes when combining terms. Always check to ensure you're applying the correct exponent rules and double-check your work at each step to avoid multiplying or adding incorrectly!