The inequality algebraically function is
.
Step 1: Write the inequality so that a rational expression
is on the left side and zero is on the right side.
\
.
Step 2: Determine the real zeros (
-intercepts of the graph )of
and the real numbers for which
is undefined.
The zeroes of the function are the values of
for which
.
The zeroes of
is
or
and
.
is defined for all values of
.
Step 3: Use the zeros and undefined values found in Step 2 to divide the real number line into intervals.
\The function is defined for all values of
except at
or
and
.
The function intervals are
.
Step 4: Select a number in each interval, evaluate
at the number, and determine whether
is positive or negative.
If
is positive, all values of
in the interval are positive. If
is negative, all values of
in the interval are negative.

The real zero of numerator is
,
and
.
\
So the real zeros are divide the
- axis into four intervals.
\
\
\
Choosing a number for
in each interval and evaluating
.
| Interval | \ \
| \
\
\
| \
Conclusion | \
| \
| \
\
| \
\
| \
Neagtive | \
| \
| \
\
| \
\
\
| \
Positive | \
| \
| \
\
| \
\
\ \ \ \ \
\ | \
Negative | \
| \
| \
\
| \
\
| \
Positive | \
\
\
\
The Solution of algebraical inequality
are in the intervals
.