\"\"

\

\

\

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:

\

\

\

The zeros of the function are the values of \"\" for which \"\".

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\"\".

\

Consider the numerator \"\".

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The zeros of \"\" are \"\".

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A rational function is undefined when denominator is zero.

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\"\"

\

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\"\" is undefined for \"\".

\

\

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\"\"

\

\

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Use the zeros and undefined values found in step 2 to divide the real number

\

line into intervals.

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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 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
\

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\"\"

\
\

\"\"

\
\

\"\"

\
Positive
\

\"\"

\
\

\"\"

\
\

\"\"

\
Positive
\

\"\"

\
\

\"\"

\
\

\"\"

\
Positive
\

\"\"

\
\

\"\"

\
\

\

\"\"

\
Negative
\

\"\"

\
\

\"\"

\
\

\"\"

\
Positive
\

\"\"

\
\

\"\"

\
\

\

\

\

\

\"\"

\
\

\

Positive

\
\

\

\"\"

\