Problem 29E

Setting up partial fraction decompositions

Give the appropriate form of the partial fraction decomposition for the following functions.

Problem 29E

Setting up partial fraction decompositions Give the appropriate form of the partial fraction decomposition for the following functions.

Solution

Step 1

In this problem we need to find the partial fraction decomposition for

Consider

Let us first see about Partial Fractions.

When a proper rational expression is decomposed into a sum of two or more rational expressions, it is known as Partial Fractions.

Consider

… (1)

Taking LCM we get,

Thus

Since the denominators of both sides are same, we can equate the numerator.

Equating the like terms from both sides, we get

… (3)

… (4)

By solving these four linear equations, we get the value of as

Thus (1) becomes,

Thus