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The inequality function 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
.
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Consider the numerator .
The zeros of are
and
Therefore the zeros of the numerator are and
.
A rational function is undefined when denominator is zero.
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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.
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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.
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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 are and
.
The real zero of denominator is .
Since there are real zeros, divide the
- axis into four 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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Negative | \
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Positive | \
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Negitive | \
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