/ 2 | 2|
| (2 + x) |(2 + x) |
| ---------------- for ---------- < 1
| / 2\ 3
| | (2 + x) |
| 3*|1 - --------|
| \ 3 /
<
| oo
| ___
| \ `
| \ -n 2*n
| / 3 *(2 + x) otherwise
| /__,
\n = 1
-----------------------------------------
2 + x
$$\frac{\begin{cases} \frac{\left(x + 2\right)^{2}}{3 \left(1 - \frac{\left(x + 2\right)^{2}}{3}\right)} & \text{for}\: \frac{\left|{\left(x + 2\right)^{2}}\right|}{3} < 1 \\\sum_{n=1}^{\infty} 3^{- n} \left(x + 2\right)^{2 n} & \text{otherwise} \end{cases}}{x + 2}$$
Piecewise(((2 + x)^2/(3*(1 - (2 + x)^2/3)), Abs((2 + x)^2)/3 < 1), (Sum(3^(-n)*(2 + x)^(2*n), (n, 1, oo)), True))/(2 + x)