Answer the questions that follow about rational functions and their decomposition:
(i) Explain the difference between a distinct linear factor and a repeated linear factor in the denominator of a rational function. Give one example of each type.
(ii) For a proper rational function whose denominator is (x+2)(x−3)3(x2+1), write down the complete form (without numerical coefficients) of the partial‐fraction expansion that would be required.
(iii) Describe, in a logically ordered list of steps, how the unknown coefficients would be determined once the form in part (ii) is written.