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The inequality is .
Write the inequality so that a rational expression is on the left side
and zero is on the right side.
\
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Determine the real zeros of (-intercepts of the graph) and the real numbers
for which is undefined:
\
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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.
\
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is undefined for
.
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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.
\\
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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 | \ \
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Conclusion | \
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Positive | \
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Positive | \
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Positive | \
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Negative | \
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Positive | \
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\ Positive \ | \
\