partial fraction formulas with names

Question 1

(x-a) (x-b)

Answer 1

A B
——– + ——
x - a x - b

Question 2

(x-a)^2

Answer 2

A B
—– + ——–
x-a (x-a)^2

Question 3

(x-a) (x-b) (x-c)

Answer 3

A B C
—- + —— + ——
x-a x-b x-c

Question 4

(x-a)^2 (x-b)

Answer 4

A B C
—— + ——— + ——
x-a (x-a)^2 x-b

Question 5

This one is the clincher.
1
———–
x^4 - 1

Which breaks down into
(x^2 + 1) (x^2 - 1)

The right side can be broken down further by using the rule of the difference of squares… (x + 1) (x - 1)
But the left side is pretty much just what it is… (x^2 + 1)

Answer 5

A B Cx + D
—– + —— + ———-
(x+1) (x-1) (x^2 + 1)