The denominator is the only thing not factored,
so factor it
The critical numbers are the zeros of all the factors:
0,
, -1, 1, 2
Arrange them in numerical order:
-1, 0, 1,
, 2
-1, 0, 1,
, 2
and put them on a number line:
-----------o----o----o--o-o------
-3 -2 -1 0 1 2 3
Choose test values less than the least, in between
them, and greater than the greatest:
Test values: -2, -0.5, 0.5, 1.5, 1.9, 3
If the test value gives
when substituted
in the open interval which the test value is in is
part of the solution; otherwise it's not.
Substituting -2 gives 161.333... which is
,
so
is part of
the solution.
Substituting -0.5 gives 0.176... which is
,
so
is part of
the solution.
Substituting 0.5 gives 2.296... which is
,
so
is part of
the solution.
Substituting 1.5 gives -31.64... which is
,
so
is NOT part of
the solution.
Substituting 1.9 gives -596.71... which is
,
so
is NOT part of
the solution.
Substituting 3 gives 10368 which is
,
so
is part of
the solution.
The critical numbers from the numerator 0,5/3, and -1
satisfy the given inequality since "equal to 0" is allowed.
However the critical numbers from the denominator, 1 and 2,
do not.
Solution set:
Edwin