The rational expression is .

Rewrite the expression so that the numerator is not of equal or higher degree than the denominator.

Apply the long division method :

The dividend is .

The divisor is .

Therefore, can be written as .

Rewrite the expression as partial fractions with constant numerators,  and , and denominators that are the linear factors of the original denominator.

.

.

Multiply each side by  .

Equate the coefficients on the left and right side of the equation to form a system of

equations.

In other words, the coefficients of the terms on the left side of the equation must be equal

to the coefficients of the terms on the right side.

Solve the equations and .

Substiute the value in equation .

Replace and with  and  in the partial fraction decomposition.

The partial fraction decomposition of the rational expression is .