1/(x-1)

1/(x-1)

Input
1/(x – 1)
Roots
(no roots exist)
Series expansion at x=0
-1 – x – x^2 – x^3 – x^4 + O(x^5)
(Taylor series)
Series expansion at x=∞
1/x + (1/x)^2 + (1/x)^3 + (1/x)^4 + O((1/x)^5)
(Laurent series)
Derivative
d/dx(1/(x – 1)) = -1/(x – 1)^2
Indefinite integral
integral 1/(-1 + x) dx = log(x – 1) + constant
Limit
lim_(x-> ± infinity) 1/(-1 + x) = 0

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