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 $2x+\frac{2}{x}=3$, then the value of $x^{3}+\frac{1}{x^{3}}+2$ is:

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{5}$

Option 3: $\frac{5}{8}$

Option 4: $\frac{7}{8}$

Question : If $x=2+\sqrt3$, then the value of $\frac{x^{2}-x+1}{x^{2}+x+1}$ is:

Option 1: $\frac{2}{3}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{4}{5}$

Option 4: $\frac{3}{5}$

Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:

Option 1: $\frac{9}{4}$

Option 2: $\frac{27}{8}$

Option 3: $\frac{5}{2}$

Option 4: $2$

Question : If $(x+\frac{1}{x})$ = 5, then the value of $\frac{5x}{x^{2}+5x+1}$ is:

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

Option 2: $\frac{1}{4}$

Option 3: $\frac{1}{2}$

Option 4: $\frac{1}{5}$