Найти область определения функции y=arccos 2x/1+x

Решите задачу:

$y=arccos\frac{2x}{1+x}\\\\OOF:\; -1 \leq \frac{2x}{1+x} \leq 1\; \to \; \left \{ {{\frac{2x}{1+x} \leq 1} \atop {\frac{2x}{1+x} \geq -1}} \right. \left \{ {{\frac{x-1}{x+1} \leq 0} \atop {\frac{3x+1}{x+1} \geq 0}}\right. \; \left \{ {{x\in (-1,1]} \atop {x\in (-\infty,-1)U[-\frac{1}{3},+\infty)}} \right. \; \to \\\\x\in [-\frac{1}{3},1]$