Thread: partial fraction from improper fraction

1. partial fraction from improper fraction

Resolve into partial fractions:

x^4 / (x^2 +1)(x^2 -1)

sorry if it looks messy but im not sure how to make fractions, etc. on this forum

anyway, since its a improper fraction i got the proper fraction by long devision and ended up with :

1 + 1/ (x^2 +1)(x^2 -1)

since i cant factorize (x^2 +1) how do i continue?

do I just say A/(x^2 +1) + B/(x^2 -1) ?

If so how do i calculate values if i have B(x^2 +1) ?

2. Originally Posted by renaldo
Resolve into partial fractions:

x^4 / (x^2 +1)(x^2 -1)

sorry if it looks messy but im not sure how to make fractions, etc. on this forum

anyway, since its a improper fraction i got the proper fraction by long devision and ended up with :

1 + 1/ (x^2 +1)(x^2 -1)

since i cant factorize (x^2 +1) how do i continue?

do I just say A/(x^2 +1) + B/(x^2 -1) ?

If so how do i calculate values if i have B(x^2 +1) ?
If a denominator has an irreducble factor of the form $\displaystyle x^2+ b^2$, then its partial fraction decomposition will have a fraction of the form $\displaystyle \frac{Ax+ B}{x^2+ b^2}$

$\displaystyle \frac{1}{(x^2+1)(x^2-1)}= \frac{Ax+ B}{x^2+ 1}+ \frac{C}{x- 1}+ \frac{D}{x+ 1}$.