I'm trying to figure out this problem:
At the moment, I've got it down to this:
To find , I let , which also gets rid of . Any ideas?
There must be a partial fraction present for each power of less than or equal to n. We can find B, but not A using Heaviside's method. Only the constant corresponding to can be found using this method.
First, multiply the original proper fraction by and evaluate the result at x = c to get the value of the constant.
To find the other constant, multiply both sides by the least common denominator to clear the fractions:
This leads to:
The polynomial on the left of the equal sign must have the same coefficient and constant as the polynomial on the right of the equal sign.
You could also say
You still get
The decomposition is: