The inequality is
.
Step 1: The exclude value for this inequality is
.
Step 2:
\Solve the related equation.
\
(Original equation)
The LCD for the term is
.
(Multiply by LCD)
(Divide common factors)
(Multiply)
(Combine like terms)
(Divide each side by
)
(Cancel common terms)
Step 3:
\Draw vertical line at the excluded value and at the solutions to separate the number line into intervals.
\Graph:
\Graph the number line.
\
Step 4: Test values are in each interval to determine the values of interval satisfy the inequality.
\Case (i):
\Test
.
(Original inequality)
(Substitute
)
(Simplify)
(LCD is
)
(Add the numerator)
(Simplify)
Case (ii):
\Test
.
(Original inequality)
(Substitute
)
(Simplify)
(LCD is
)
(Add the numerator)
(Simplify)
Case (iii):
\Test
.
(Original inequality)
(Substitute
)
(Simplify)
(LCD is
)
(Add the numerator)
(Simplify)
The statement is true for
and
.
Therefore the solution is
or
.
The solution is
.