// 2 x \ // 2 x \
// 2 x \ || - - + - | || - - + - | // 2 x \
|| - - + - | || 3 3 | 2 x| | || 3 3 | 2 x| | || - - + - |
|| 3 3 | 2 x| | || -------- for |- - + -| < 1| || -------- for |- - + -| < 1| || 3 3 | 2 x| |
|| ------- for |- - + -| < 1| || 2 | 3 3| | || 2 | 3 3| | || ------- for |- - + -| < 1|
|| 5 x | 3 3| | || /5 x\ | || /5 x\ | || 5 x | 3 3| |
|| - - - | || |- - -| | || |- - -| | || - - - |
|| 3 3 | || \3 3/ | || \3 3/ | || 3 3 |
- 4*|< | - 2*|< | + x*|< | + 2*x*|< |
|| oo | || oo | || oo | || oo |
|| ___ | || ___ | || ___ | || ___ |
|| \ ` | || \ ` | || \ ` | || \ ` |
|| \ -n n | || \ -n n | || \ -n n | || \ -n n |
|| / 3 *(-2 + x) otherwise | || / n*3 *(-2 + x) otherwise | || / n*3 *(-2 + x) otherwise | || / 3 *(-2 + x) otherwise |
|| /__, | || /__, | || /__, | || /__, |
\\n = 1 / ||n = 1 | ||n = 1 | \\n = 1 /
\\ / \\ /
$$x \left(\begin{cases} \frac{\frac{x}{3} - \frac{2}{3}}{\left(\frac{5}{3} - \frac{x}{3}\right)^{2}} & \text{for}\: \left|{\frac{x}{3} - \frac{2}{3}}\right| < 1 \\\sum_{n=1}^{\infty} 3^{- n} n \left(x - 2\right)^{n} & \text{otherwise} \end{cases}\right) + 2 x \left(\begin{cases} \frac{\frac{x}{3} - \frac{2}{3}}{\frac{5}{3} - \frac{x}{3}} & \text{for}\: \left|{\frac{x}{3} - \frac{2}{3}}\right| < 1 \\\sum_{n=1}^{\infty} 3^{- n} \left(x - 2\right)^{n} & \text{otherwise} \end{cases}\right) - 2 \left(\begin{cases} \frac{\frac{x}{3} - \frac{2}{3}}{\left(\frac{5}{3} - \frac{x}{3}\right)^{2}} & \text{for}\: \left|{\frac{x}{3} - \frac{2}{3}}\right| < 1 \\\sum_{n=1}^{\infty} 3^{- n} n \left(x - 2\right)^{n} & \text{otherwise} \end{cases}\right) - 4 \left(\begin{cases} \frac{\frac{x}{3} - \frac{2}{3}}{\frac{5}{3} - \frac{x}{3}} & \text{for}\: \left|{\frac{x}{3} - \frac{2}{3}}\right| < 1 \\\sum_{n=1}^{\infty} 3^{- n} \left(x - 2\right)^{n} & \text{otherwise} \end{cases}\right)$$
-4*Piecewise(((-2/3 + x/3)/(5/3 - x/3), |-2/3 + x/3| < 1), (Sum(3^(-n)*(-2 + x)^n, (n, 1, oo)), True)) - 2*Piecewise(((-2/3 + x/3)/(5/3 - x/3)^2, |-2/3 + x/3| < 1), (Sum(n*3^(-n)*(-2 + x)^n, (n, 1, oo)), True)) + x*Piecewise(((-2/3 + x/3)/(5/3 - x/3)^2, |-2/3 + x/3| < 1), (Sum(n*3^(-n)*(-2 + x)^n, (n, 1, oo)), True)) + 2*x*Piecewise(((-2/3 + x/3)/(5/3 - x/3), |-2/3 + x/3| < 1), (Sum(3^(-n)*(-2 + x)^n, (n, 1, oo)), True))