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

\(\frac{2 x^{2}+3}{\left(x^{2}-8 x+16\right)\left(x^{2}+3 x+4\right)}\)

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