Could someone please show me how to solve the following types of Partial Fractions with full working out:
a). 1 / (x + 2)^2 (x-1)
b). x + 2 / x^2(x-4)
c). 9 / (x - 1)(x^2+1)
d). 2x + 1 / x(x^2 + 4)
set ups ...
a) $\displaystyle \frac{1}{(x+2)^2(x-1)} = \frac{A}{x+2} + \frac{B}{(x+2)^2} + \frac{C}{x-1}$
b) $\displaystyle \frac{x+2}{x^2(x-4)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-4}$
c) $\displaystyle \frac{9}{(x-1)(x^2+1)} = \frac{A}{x-1} + \frac{Bx+C}{x^2+1}$
d) $\displaystyle \frac{2x+1}{x(x^2+4)} = \frac{A}{x} + \frac{Bx+C}{x^2+4}$
... I leave the "full working out" to you.