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 $(x+\frac{1}{x})$ = 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: $\frac{1}{5}$

Question : If $x+\frac{1}{x}=-14$, and $x<-1$, what will be the value of $x^2-\frac{1}{x^2}$?

Option 1: $-112 \sqrt{3}$

Option 2: $112 \sqrt{3}$

Option 3: $-140 \sqrt{2}$

Option 4: $140 \sqrt{2}$

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: $0$