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

Option 1: $\frac{3}{8}$

Option 2: $\frac{13}{12}$

Option 3: $\frac{4}{9}$

Option 4: $\frac{11}{13}$

Question : If $2x-\frac{2}{x}=1(x \neq 0)$, then the the value of $(x^3-\frac{1}{x^3})$ is:

Option 1: $\frac{13}{4}$

Option 2: $\frac{13}{8}$

Option 3: $\frac {17}{4}$

Option 4: $\frac{17}{8}$

Question : If $(x + \frac{1}{x})$ = 6, then the value of ($x^{2} + \frac{1}{x^{2}}$) is:

Option 1: 23

Option 2: 16

Option 3: 34

Option 4: 32

Question : If $\left(x-\frac{1}{x}\right)^2=12$, what is the value of $\left(x^2-\frac{1}{x^2}\right)$, given that $x>0$?

Option 1: $6 \sqrt{2}$

Option 2: $8 \sqrt{3}$

Option 3: $6 \sqrt{3}$

Option 4: $8 \sqrt{2}$

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

Option 1: $1$

Option 2: $\frac{3}{7}$

Option 3: $\frac{2}{3}$

Option 4: $0$