Simplify: 11−x+11+x+21+x2+41+x4\frac{1}{1-x} + \frac{1}{1+x} + \frac{2}{1+x^2} + \frac{4}{1+x^4}1−x1+1+x1+1+x22+1+x44 for ∣x∣<1|x| < 1∣x∣<1.
81−x8\frac{8}{1-x^8}1−x88
8x1−x8\frac{8x}{1-x^8}1−x88x
81+x8\frac{8}{1+x^8}1+x88
11−x4\frac{1}{1-x^4}1−x41