Question : If $x+\frac{1}{x}=6$, then find the value of $\frac{3 x}{2 x^2-5 x+2}$.

Question : If $x-\frac{3}{x}=6, x \neq 0$, then the value of $\frac{x^4-\frac{27}{x^2}}{x^2-3 x-3}$ is:

Question : If $x+5+\frac{1}{x+1}=6$, then the value of $(x+1)^{3}+\frac{1}{(x+1)^{3}}$ is:

Question : If $x+\frac{1}{x}=\sqrt{3}$, then the value of $x^{3}+\frac{1}{x^{3}}$ is equal to:

Question : If $x-\frac{1}{x}=5, x \neq 0$, then what is the value of $\frac{x^6+3 x^3-1}{x^6-8 x^3-1} ?$