Question

plz.simply with detail ​

Answer 1

Answer:

$\frac{1}{x - 1} - \frac{1}{x + 1} - \frac{2}{x^{2} + 1} - \frac{4}{x ^{4} + 1} \\ = \frac{(x + 1) - (x - 1)}{(x - 1)(x + 1)} - \frac{2}{x^{2} + 1} - \frac{4}{x ^{4} + 1} \\= \frac{x + 1 - x + 1}{x ^{2} - 1} - \frac{2}{x^{2} + 1} - \frac{4}{x ^{4} + 1} \\= \frac{2}{x ^{2} - 1} - \frac{2}{x^{2} + 1} - \frac{4}{x ^{4} + 1}\\= \frac{2(x^{2} + 1) - 2(x^{2} - 1)}{(x ^{2} - 1)(x^{2} + 1)} - \frac{4}{x ^{4} + 1} \: \\= \frac{2x^{2} + 2 - 2x^{2} + 2}{x ^{4} - 1} - \frac{4}{x ^{4} + 1} \: \\= \frac{4}{x ^{4} - 1} - \frac{4}{x ^{4} + 1} \: \\= \frac{4(x ^{4} + 1) - 4(x ^{4} - 1)}{(x ^{4} - 1)(x ^{4} + 1)} \: \\= \frac{4x ^{4} + 4 - 4x ^{4} + 4}{x ^{8} - 1} \: \\ = \frac{8}{x ^{8} - 1}$