10.1. The numbers $a$ and $b$ are such that $|a| \neq|b|$ and $\frac{a+b}{a-b}+\frac{a-b}{a+b}=6$. Find the value of the expression $\frac{a^{3}+b^{3}}{a^{3}-b^{3}}+\frac{a^{3}-b^{3}}{a^{3}+b^{3}}$.
Answer: 18/7. From the ratio $\frac{a+b}{a-b}+\frac{a-b}{a+b}=6$, after bringing to a common denominator and transformations in the numerator, we get the ratio $\frac{2 a^{2}+2 b^{2}}{a^{2}-b^{2}}=6$ or $a^{2}=2 b^{2}$. The expression $\frac{a^{3}+b^{3}}{a^{3}-b^{3}}+\frac{a^{3}-b^{3}}{a^{3}+b^{3}}$ after bringing to a common denominator and transformations in the numerator takes the form $\frac{2 a^{6}+2 b^{6}}{a^{6}-b^{6}}$. Replacing $a^{2}$ with $2 b^{2}$, we get $\frac{2\left(2 b^{2}\right)^{3}+2 b^{6}}{\left(2 b^{2}\right)^{3}-b^{6}}=\frac{18}{7}$.

Comment. Obtaining the answer for specific values of $a, b$ is evaluated at no more than 2 points.