\
\
The inequality is
.
Write the inequality so that a rational expression
is on the left side
and zero is on the right side.
\
\
Determine the real zeros of (
-intercepts of the graph) and the real numbers
for which
is undefined:
\
\
The zeros of the function are the values of
for which
.
.
Consider the numerator
.
The zeros of
are
.
A rational function is undefined when denominator is zero.
\
\
is undefined for
.
\
\
\
\
Use the zeros and undefined values found in step 2 to divide the real number
\line into intervals.
\Denominator of the function should not be zero.
\\
\
The function is defined for all values of
except at
.
The function intervals are
and
.
\
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 zeros of numerator is
and
the real zeros of denominator
are
and
.
\
Since there are
real zeros divide the
-axis into six intervals.
The hallow circle represents the real zeros of the numerator.
\The solid circle represents the real zeros of the denominator.
\\
Choose a number for
in each interval and evaluate
.
| Interval | \ \
\ \
\ | \
\
\
| \
Conclusion | \
| \
\
| \
\
| \
\
| \
Positive | \
| \
| \
\
| \
\
| \
Positive | \
| \
| \
\
| \
\
| \
Positive | \
| \
| \
\
| \
\
\
| \
Negative | \
| \
| \
\
| \
\
| \
Positive | \
| \
| \
\
| \
\
\ \ \ \
| \
\
\ Positive \ | \
\