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

Question : If $5x+\frac{1}{x}=10$, then $x^2+\frac{1}{25x^2}$ is equal to:

Question : If $\frac{5x}{2}-\frac{[7(6x-\frac{3}{2})]}{4}=\frac{5}{8}$, then what is the value of $x$?

Question : If $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

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