Exercise about ashymptotes (limits)

Hi guys, hoy are you?
I don´t understand how to solve an exercise of limits :_
It says:
Determine vertical asymptotes, horizontal and oblique.
a) f(x)= (x - 1)/(|x| - 1)

b) f(x)= ln[(x^2) - 4)

c) y= (1/(e^x) - 1)


Thank you very much!!!!

(a)
f(x) = (x - 1)/(|x| - 1)

For x < 0: f(x) = (x - 1)/(-x - 1) = (1 - x)/(1 + x)
For x ≥ 0: f(x) = (x - 1)/(x - 1) = 1

When x→-1, f(x) = (1 - x)/(1 + x)→±∞: x =-1 is a vertical asymptote.
When x→-∞, f(x) = (1 - x)/(1 + x)→ 0 : y = 0 is a horizontal asymptote.

b)
f(x) = ln(x² - 4)
f(x) is defined for x such that x² - 4 > 0, or equivalently
x < -2 or x > 2.
When x→-2⁻ , f(x)→∞: x =-2 is a vertical asymptote.
When x→ 2⁺ , f(x)→∞: x = 2 is another vertical asymptote.

c)
y= 1/(e^x - 1)

When x→±∞, f(x)→0: y = 0 is the horizontal asymptote.
When x→ 0 , f(x)→∞: x = 0 is the vertical asymptote

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