I'm glad you put those parentheses there.  Most students would
have written  " x+2/x+3 " which really means , an
altogether different expression.

But you didn't state what you were to find.  I assume it is 
the domain and range.

The denominator x+3 must not equal 0, so

x+3 ≠ 0
  x ≠ -3,  so we have a vertical asymptote at x = -3

The degree of the numerator and denominator are both 1, so
the horizontal asymptote is

y = 

y = 

y = 1 , so we have a horizontal asymptote at y = 1

You also state "x is not equal to 0", so we must leave out the
point (0,) and put an open circle there. The two asymptotes
are in green:



So the domain is (-∞,-3)U(-3,0)U(0,∞) and

the range is (-∞,)U(,1)U(1,∞)

Edwin