2/(1-x^2) + 2/(1+x^2) + 4/(1+x^4)

asked by guest
on Jan 20, 2025 at 11:16 pm



You asked:

Evaluate the expression: \(\frac{2}{1 - {x}^{2}} + \frac{2}{1 + {x}^{2}} + \frac{4}{1 + {x}^{4}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{2}{1 - {x}^{2}} + \frac{2}{1 + {x}^{2}} + \frac{4}{1 + {x}^{4}} = \frac{4}{x^{4} + 1} + \frac{2}{x^{2} + 1} + \frac{2}{1 - x^{2}} \)

Factored

\[\frac{2}{1 - {x}^{2}} + \frac{2}{1 + {x}^{2}} + \frac{4}{1 + {x}^{4}} = - \frac{8}{\left(x^{2} + 1\right) \left(x^{4} + 1\right) \left(x - 1\right) \left(x + 1\right)}\]

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