can someone help me determine that limit for the following function, as x --> -2?

Question

2 - abs(x) / 2 + x

Answer 1

Please be sure to enclose numerators and denominators in parentheses when transcribing fractions. The given expression does not equal to
(2-abs(x))/(2+x), which I will assume is the correct form.

f(x) = (2-abs(x))/(2+x)
is the same as
f(x)=(2-x)/(2+x) when x∈[0,∞)
f(x)=(2+x)/(2+x) when x∈(-∞,-2)∪(-2,0)

As x→-2,
f(x)=(2+x)/(2+x)
which equals 1 by long division.
Therefre
Lim x→-2 f(x) = 1