The limit problem of Higher Mathematics Why is LIM (x → 1 -) e1 / X-1 = 0

The limit problem of Higher Mathematics Why is LIM (x → 1 -) e1 / X-1 = 0

X tends to 1-
So X-1 tends to zero-
So 1 / (x-1) tends to be negative infinity
So the negative infinite power of e tends to zero
So limit = 0