Get 0 on the right:



Write  as  



Get the LCD of (x+2) and
multiply top and bottom of
 by that:





Combine the numerators over the LCD:



Remove the parentheses in the top:



Combine like terms:



Find the critical values by setting both
the numerator and the denominator equal to
zereo and solving:

 gives critical value 

 gives critical value 

Indicate the critical values on a number line:

 -------------o-------------------o------------------------
 -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4

Choose a number left of -7, say -8.
Substitute it into the original or the factored form.
It's easier to use the factored form:






 




That is false so we do not shade the part
to the left of .  We still have the
number line

 -------------o-------------------o------------------------
 -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4


Choose a number between -7 and -2, say -3.
Substitute it into the original or the factored form.
It's easier to use the factored form:






 




That is true so we do shade the part between 
and .

 -------------o===================o------------------------
 -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4

Choose a number right of -2, say 0.
Substitute it into the original or the factored form.
It's easier to use the factored form:






 




That is false so we do not shade the part
to the right of .  We end up with the
number line

 -------------o===================o------------------------
 -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4

We need only test the endpoints of the interval when the
symbol of inequality is < or >.

The answer in interval notation is (-7,-2).

Edwin