Express \( \frac{(x+2)^2}{x^2(x-2)} \) as the sum of 3 partial fractions.
Take note that \( x^2 \) is a repeated factor
\( \begin{aligned} \frac{(x+2)^2}{x^2(x-2)}=\frac{x^2+4 x+4}{x^2(x-2)} \\ \text { Let } \frac{x^2+4 x+4}{x^2(x-2)} =\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-2} \\ \quad x^2+4 x+4 =A x(x-2)+B(x-2)+C x^2\end{aligned}\)
Find values of \( A \) and \( B \) by substituting suitable values of \( x \)
To find \( B \), sub \( x = 0 \)
To find \( C \), sub \( x = 2 \)
Now that we know \( B \) and \( C \), sub \( x = 1 \) to find \( A \)