Question

write the partial fraction decomposition of the rational expression.

Answer 1

Step 1:

The partial fraction is .

The partial fraction decomposition :

Multiply each side by .

Step 2:

Compare coefficients on each side.

                               equation (1)

Compare coefficients on each side.

                equation (2)

Compare coefficients on each side.

        equation (3)

Compare constants on each side.

            equation (4)

Substitute equation (1) in equation (2).

                   equation (5)

Answer 2

Contd....

Step 3:

Substitute equation (5) and equation (1) in equation (4).

Substitute in the equation (1).

Substitute in equation (5).

                       equation (6)

Substitute and in equation (3).

                       equation (7)

Add equation (6) and equation (7).

Substitute in equation (6).

Substitute in the partial fraction decomposition.

Solution :

.