Key to "Find the limits limx→01x−1+1x+1x" - Plainmath

Tazmin Horton

Answered question

2020-11-07

Find the limits

lim_{x \to 0} \frac{\frac{1}{x - 1} + \frac{1}{x + 1}}{x}

Answer & Explanation

Khribechy

Skilled2020-11-08Added 100 answers

Given that

lim_{x \to 0} \frac{\frac{1}{x - 1} + \frac{1}{x + 1}}{x}

Compute the limit as follows.

lim_{x \to 0} \frac{\frac{1}{x - 1} + \frac{1}{x + 1}}{x} = lim_{x \to 0} \frac{x + 1 + x - 1}{x (x - 1) (x + 1)}

= lim_{x \to 0} \frac{2 x}{x (x^{2} - 1)}

= lim_{x \to 0} \frac{2}{(x^{2} - 1)}

= \frac{2}{0 - 1}

= - 2

Thus,

lim_{x \to 0} \frac{\frac{1}{x - 1} + \frac{1}{x + 1}}{x} = - 2

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