(a) Include a constant term: \[f(x)=A+\frac B{3x-2}+\frac C{x+6}.\] The leading coefficient gives \(A=4\). Subtracting the denominator times 4, \[-9x+46=B(x+6)+C(3x-2).\] At \(x=2/3\), \(B=6\); at \(x=-6\), \(C=-5\). Thus \[f(x)=4+\frac6{3x-2}-\frac5{x+6}.\]

(b) Expand as geometric series: \[\begin{aligned}f(x)&=4-3\left(1-\frac32x\right)^{-1}-\frac56\left(1+\frac x6\right)^{-1}\\&=4-3\left(1+\frac32x+\frac94x^2\right)-\frac56\left(1-\frac x6+\frac{x^2}{36}\right)+\cdots\\&=\frac16-\frac{157}{36}x-\frac{1463}{216}x^2+\cdots.\end{aligned}\] The common validity condition is \(|x|<2/3\).