If x + 1/x = 3 , then the value of 3x^2 - 4x + 3x^2 - x + 1 is?

Answer: Option C

$$\begin{array}{rl}& x+\frac{1}{x}=3\\ & \frac{3x^2-4x+3}{x^2-x+1}\\ & =\frac{\frac{3x^2}{x}-\frac{4x}{x}+\frac{3}{x}}{\frac{x^2}{x}-\frac{x}{x}+\frac{1}{x}}\\ & =\frac{3\left(x+\frac{1}{x}\right)-4}{\left(x+\frac{1}{x}\right)-1}\\ & =\frac{3\times 3-4}{3-1}\\ & =\frac{9-4}{2}\\ & =\frac{5}{2}\end{array}$$