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

Answer: Option B

$$\begin{array}{rl}& \frac{x^2-x+1}{x^2+x+1}=\frac{3}{2}\left(\text{Given}\right)\\ & \Rightarrow \frac{x\left\{\left(x+\frac{1}{x}\right)-1\right\}}{x\left\{\left(x+\frac{1}{x}\right)+1\right\}}=\frac{3}{2}\\ & \Rightarrow \frac{\left(x+\frac{1}{x}\right)-1}{\left(x+\frac{1}{x}\right)+1}=\frac{3}{2}\\ & \text{Let }\left(x+\frac{1}{x}=y\right)\\ & \Rightarrow \frac{y-1}{y+1}=\frac{3}{2}\\ & \Rightarrow 2\left(y-1\right)=3\left(y+1\right)\\ & \Rightarrow 2y-2=3y+3\\ & \Rightarrow y=-2-3\\ & \Rightarrow y=-5\\ & \therefore x+\frac{1}{x}=-5\\ & \end{array}$$