If x + 1/x = 3 , then the value of x^3 + 1/xx^2 - x + 1\, is?

Answer: Option C

$$\begin{array}{rl}& x+\frac{1}{x}=3\left(\text{Given}\right)\\ & \frac{x^3+\frac{1}{x}}{x^2-x+1}\left(\text{Divide by }x\right)\\ & \Rightarrow \frac{\frac{x^3}{x}+\frac{1}{x^2}}{\frac{x^2}{x}-\frac{x}{x}+\frac{1}{x}}\\ & \Rightarrow \frac{x^2+\frac{1}{x^2}}{x-1+\frac{1}{x}}\\ & \Rightarrow \frac{x^2+\frac{1}{x^2}}{x+\frac{1}{x}-1}\\ & \therefore x+\frac{1}{x}=3\\ & \therefore x^2+\frac{1}{x^2}=9-2=7\\ & \therefore \frac{x^2+\frac{1}{x^2}}{x+\frac{1}{x}-1}=\frac{7}{3-1}=\frac{7}{2}\end{array}$$