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)

                 (Subtract from each side)

                                   (Apply additive imverse property: )

                                (Factors)

and                              (Simplify)

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 )

                                        (Subtract the numerator)

                                 (Simplify)

Case (ii):

Test .

                                    (Original inequality)

                                    (Substitute )

                                               (Simplify)

                                         (Simplify)

Case (iii):

Test .

                                    (Original inequality)

                                    (Substitute )

                                          (Simplify)

                                          (LCD is )

                                                  (Add the numerator)

                                                 (Simplify)

Case (iv):

Test .

                                   (Original inequality)

                                   (Substitute )

                                         (Simplify)

                                          (LCD is )

                                                  (Subtract the numerator)

                                                   (Simplify)

The statement is true for and .

Therefore the solution is or .

The solution is or .