Step 1 :
\The rational inequality is
.
State the exclude values, those are the values for which the denominator is zero.
\The exclude value of the inequality is 3.
\Step 2 :
\Solve the related equation
.
Solution of related equation
.
Step 3 :
\Draw the vertical lines at the exclude values and at the solution to separate the number line into intervals.
\
Step 4 :
\Now test sample values in each interval to determine whether the values in the interval satisfy the inequality.
\| Test interval | \ - value | \
Inequality | \Conclusion | \
![]() | \
![]() | \
![]() | \
True | \
![]() | \
![]() | \
![]() | \
False | \
![]() | \
![]() | \
![]() | \
True | \
Step 5 :
\Since the original inequality contains a
symbol, exclude it into set of solutions at
.

Since the above statement is true,
is a solution of inequality.
Conclude that the inequality is satisfied for all
- values in
and
.
Solution of the inequality
is
.