((1)/(x-1)+(1)/(x+1))/(x)

asked by guest
on Jan 26, 2025 at 7:34 am



You asked:

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

MathBot Answer:

Evaluated



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

Expanded

\[\frac{\frac{1}{x - 1} + \frac{1}{x + 1}}{x} = \frac{1}{x^{2} + x} + \frac{1}{x^{2} - x}\]

Factored

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

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