(i) Express \(\frac{5x + 3}{(x + 1)^2(3x + 2)}\) in partial fractions as:

\(\frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{C}{3x+2}\)

Equating and solving for constants, we find \(A = 1, B = 2, C = -3\).

(ii) Expand each term:

\(\frac{1}{(x+1)^2} = (1 + x)^{-2} \approx 1 - 2x + 3x^2\)

\(\frac{1}{3x+2} = \frac{1}{2}(1 - \frac{3}{2}x + (\frac{3}{2}x)^2) \approx \frac{1}{2} - \frac{3}{4}x + \frac{9}{8}x^2\)

Combine and simplify:

\(\frac{5x + 3}{(x + 1)^2(3x + 2)} \approx \frac{3}{2} - \frac{11}{4}x + \frac{29}{8}x^2\)