The expression 1x - 1 - 1x + 1 - 2x^2 + 1 - 4x^4 + 1 is equal to = ?

Answer: Option B

$$\begin{array}{rl}& \text{Given expression,}\\ & \left(\frac{1}{x-1}-\frac{1}{x+1}\right)-\frac{2}{x^2+1}-\frac{4}{x^4+1}\\ & =\left[\frac{\left(x+1\right)-\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\right]-\frac{2}{x^2+1}-\frac{4}{x^4+1}\\ & =\left(\frac{2}{x^2-1}-\frac{2}{x^2+1}\right)-\frac{4}{x^4+1}\\ & =\left[\frac{2\left(x^2+1\right)-2\left(x^2-1\right)}{\left(x^2-1\right)\left(x^2+1\right)}\right]-\frac{4}{x^4+1}\\ & =\frac{4}{x^4-1}-\frac{4}{x^4+1}\\ & =\frac{4\left(x^4+1\right)-4\left(x^4-1\right)}{\left(x^4-1\right)\left(x^4+1\right)}\\ & =\frac{8}{x^8-1}\end{array}$$