Division by zero is not defined in mathematics

So denominators can never be zero, so

The denominator x+2 can never equal to 0,

so we write x+2 ≠ 0 and solve for x
              x ≠ -2

The denominator x+1 also can never equal to 0,

so we write x+1 ≠ 0 and solve for x
              x ≠ -1

On a number line like this 

--------------------------------
-6 -5 -4 -3 -2 -1  0  1  2  3  4

We put open circles at -2 and -1

-------------o--o---------------
-6 -5 -4 -3 -2 -1  0  1  2  3  4

and shade the rest, putting arrows at the ends,
pointing to negative infinity on the left and to
positive infinity on the right:

<============o==o==============>
-6 -5 -4 -3 -2 -1  0  1  2  3  4

The interval notation is an abbreviation of the
above number-line graph:



Edwin