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 $x+\frac{1}{x}=1$, then the value of $\frac{x^2+7x+1}{x^2+11x+1}$:

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

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

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

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

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

Option 1: $\frac{8}{27}$

Option 2: $\frac{61}{27}$

Option 3: $\frac{62}{27}$

Option 4: $\frac{52}{27}$

Question : The value of $(x^{\frac{1}{3}}+x^{-\frac{1}{3}})(x^{\frac{2}{3}}-1+x^{-\frac{2}{3}})$ is:

Option 1: $x^{-1}+x^{\frac{2}{3}}$

Option 2: $x+x^{-\frac{1}{3}}$

Option 3: $x^{\frac{1}{3}}+x^{–1}$

Option 4: $x+x^{–1}$

Question : If $x^4+y^4+x^2 y^2=17 \frac{1}{16}$ and $x^2-x y+y^2=5 \frac{1}{4}$, then one of the values of $(x-y)$ is:

Option 1: $\frac{5}{2}$

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

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

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