Suppose where A, B, and C are real constants. What is \[\frac{1}{x^3-x^2-21x+45}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}\]?
By partial fractions, (A,B,C) = (1/8, 7/32, -1/80).
