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

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

Option 2: $\frac{1}{6}$

Option 3: $5$

Option 4: $6$

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

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

Option 3: $\frac{7}{2}$

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

Question : If $\frac{1}{6}$ of $x$ – $\frac{7}{2}$ of $\frac{3}{7}$ equals to $(-\frac{7}{4})$, then the value of $x$ is:

Option 1: –1.5

Option 2: –3

Option 3: –2.5

Option 4: 6