Write out the form of the partial fraction decomposition of the function. Do not determine the numerical value of the coefficients.
a) $f(x) = \frac{x^2+x}{x^3-3x^2+2x}$
My solution: $$=\frac{x^2+x}{x(x-2)(x-1)} = \frac{A}{x} + \frac{B}{x-2} + \frac{C}{x-1}$$
b) $f(t) = \frac{t^5+1}{t^6+t^3}$
My solution: $$=\frac{t^5+1}{t^3(t^3+1)} = \frac{At^2+Bt+C}{t^3+1} + \frac{D}{t^3}$$
c) $f(x) = \frac{x^5+1}{(x^2-x)(x^4+2x^2+1)}$
My solution: $$=\frac{x^5+1}{x(x-1)(x^2+1)^2} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{E}{x} + \frac{F}{x-1}$$
Are they correct?
In part B you need to add a factor over $t^2$ and a factor over $t$.