If x - 1/x = 5, x ≠ 0, then what is the value of x^6 + 3x^3 - 1x^6 - 8x^3 - 1?

Answer: Option B

$$\begin{array}{rl}& \text{Given, }x-\frac{1}{x}=5\\ & \Rightarrow x^3-\frac{1}{x^3}=5^3+3\times 5=140\\ & \frac{x^6+3x^3-1}{x^6-8x^3-1}\\ & =\frac{x^3+3-\frac{1}{x^3}}{x^3-8-\frac{1}{x^3}}\\ & =\frac{x^3-\frac{1}{x^3}+3}{x^3-\frac{1}{x^3}-8}\\ & =\frac{140+3}{140-8}\\ & =\frac{143}{132}\\ & =\frac{13}{12}\end{array}$$