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 $x+\frac{1}{x}=6$, 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: $0$

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:

Option 1: 80

Option 2: 270

Option 3: 54

Option 4: 90

Question : If $x^{4}+\frac{1}{x^{4}}=34$, what is the value of $x^{3}-\frac{1}{x^{3}} $?

Option 1: 0

Option 2: 6

Option 3: 8

Option 4: 14

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

Option 1: 2

Option 2: 0

Option 3: –2

Option 4: 4