The rational expression is .

In the above expression is improper, so solve by the long division method.

Divide the first term of the dividend by the first term of the divisor .

So,the first term of the quotient is 2x.Multiply by 2x and subtract.

The result of the division is .

The denominator of remainder factors as , so m = 3.

The form of decomposition of expression is .                    (Write form of decomposition)

                      (Multiply each side by )

Let substitute in the above basic equation.

                      (Write basic equation)

(Substitute )

                                                                               (Simplify)

                                                                                   (Divide each side by 4)

Let substitute in the above basic equation.

                         (Write basic equation)

(Substitute )

                                                                                (Simplify)

                                                                                  (Divide each side by negative 2)

Let substitute in the above basic equation.

                         (Write basic equation)

    (Substitute )

                                                                   (Simplify)

                                                                 (Substitute )

                                                                          (Simplify)

                                                                                  (Subtract 26 from each side)

                                                                                    (Divide each side by 3)

So, the partial fraction decomposition is .

The partial fraction decomposition is .