The inequality algebraically function is .
Step 1: Write the inequality so that a rational expression is on the left side and zero is on the right side.
\
.
Step 2: Determine the real zeros (-intercepts of the graph) off and the real numbers for which
is undefined.
The zeroes of the function are the values of for which
.
The zeroes of is
.
A rational function is undefined when denominator is zero.
\ is undefined for
or
.
Step 3: 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
or
.
The function intervals are .
Step 4: 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 zero of numerator is and the real zeros of denominator
or
\
So the real zeros are divide the - axis into four intervals.
\
\
\
Choosing a number for in each interval and evaluating
.
Interval | \ \
| \
\
\ | \
conclusion | \
\
| \
\
| \
\
| \
negative | \
\
| \
\
| \
\
| \
positive | \
\
| \
\
| \
\
\ | \
negative | \
\
| \
\
| \
\
\ \ \ \ | \
positive | \
\
\
\
The inequality algebraically function is and intevals are
.