How do I find the partial fraction decomposition of #(x^4)/(x^4-1)# ?
1 Answer
By Partial Fraction Decomposition, we can write
Let us look at some details.
By rewriting a bit,
Let us find the partial fractions of
by factoring out the denominator,
by splitting into the partial fraction form,
by taking the common denominator,
by simplifying the numerator,
Since the numerator is originally 1, by matching the coefficients,
(1)
(2)
(3)
(4)
By adding (1) and (3),
(5)
By adding (2) and (4),
(6)
By adding (5) and (6),
(7)
By plugging (7) into (5),
(8)
By plugging (7) and (8) into (1),
(9)
By plugging (7) and (8) into (2),
(10)
By (5), (6), (9), and (10),