If x - 1/x = 1 , then the value of x^4 - 1x^23x^2 + 5x - 3 = ?

Answer: Option B

$$\begin{array}{rl}& x-\frac{1}{x}=1\\ & \Rightarrow \frac{x^4-\frac{1}{x^2}}{3x^2+5x-3}\\ & \text{Divide and multiply by }x\\ & \Rightarrow \frac{\frac{x^4}{x}-\frac{1}{x^3}}{\frac{3x^2}{x}+\frac{5x}{x}-\frac{3}{x}}\\ & \Rightarrow \frac{x^3-\frac{1}{x^3}}{3x+\frac{3}{x}+5}\\ & \Rightarrow \frac{x^3-\frac{1}{x^3}}{3\left(x-\frac{1}{x}\right)+5}\\ & \Rightarrow x-\frac{1}{x}=1\\ & \text{Take cube on both sides}\\ & \Rightarrow {\left(x-\frac{1}{x}\right)}^3={\left(1\right)}^3\\ & \Rightarrow x^3-\frac{1}{x^3}-3\left(x-\frac{1}{x}\right)=1\\ & \Rightarrow x^3-\frac{1}{x^3}-3\left(1\right)=1\\ & \Rightarrow x^3-\frac{1}{x^3}=4\\ & \Rightarrow \frac{x^3-\frac{1}{x^3}}{3\left(x-\frac{1}{x}\right)+5}\\ & \Rightarrow \frac{4}{3\times 1+5}\\ & \Rightarrow \frac{4}{8}\\ & \Rightarrow \frac{1}{2}\end{array}$$