Question

There are two ways to find the unknown coefficients of partial fraction decomposition. The second method...

There are two ways to find the unknown coefficients of partial fraction decomposition. The second method involves using "nice" values of x that are actually zeros of the denominator. So, the rational function we want to decompose is undefined for them, nevertheless, this method works, why?

Homework Answers

Answer #1

We use zeros of the denominator after getting rid of denominators

so, there won't be any denominator on any side

so, it can not be undefined

For example:

We use zeros of denominators after we cancel denominator both sides

so, we can multiply both sides (x-1)(x+1)

now, we can choose zeros of the denominator

It won't be undefined because there is no denominator now

First zero:

Second zero:

now, we can plug it back

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