The partial fraction decomposition of (5x+1)/((x-1)(x+1)(x+2)) is given by A/(x-1)+B/(x+1)+C/(x+2) . What are the constants of A, B, and C?
2 Answers
Explanation:
.
This means:
Comparing coefficients, we get:
We have three equations and three unknowns.
Let's multiply the first equation by
Let's add it to the third equation:
From the second equation:
Let's plug these into the first equation:
While the answer in https://socratic.org/s/aQEPEWkD is perfect and the method works in general, there is a shortcut that works rather well in examples like this one - in which all the factors of the denominator are monomials.
Explanation:
Starting with
multiply both sides by
Since this is an identity, it should be valid for all values of
- substituting
x=1 , gives
- substituting
x=-1 , gives
- substituting
x=-2 , gives