\"\"

\

\

\

The inequality function 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 \"\" and \"\".

\

Since \"\" are imiginary roots these are not to be considered.

\

Therefore the zeros of the numerator are \"\" and \"\".

\

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 are \"\" and \"\".

\

The real zeros of denominator are \"\" and \"\".

\

\

Since there are \"\" real zeros, divide the \"\"- axis into five 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
\

\

\"\".