Classification discussion: both of them are greater than 0, that is, (X+ 1) times (2X+ 1) is greater than 0.

X is less than-1 or greater than -0.5.

Both are less than 0, that is, (X+ 1) times (2X+ 1) is less than 0.

X is greater than-1 and less than -0.5.

Note: Never multiply the denominator for such questions. Division can be equivalent to multiplication, and it can be solved according to the law that it is greater than taking two sides and less than taking the middle.

Study hard, come on