1)
$\Leftrightarrow \left\{ \begin{array}{l} 2x+1\geq 0\\ \frac{x+1}{2-x} \geq 0\\2x+1\leq \frac{4(x^2+2x+1)}{4-4x+x^2}\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} x\geq -\dfrac{1}{2}\\ -1\leq x< 2\\2x^3-11x^2-4x\leq 0\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} -\dfrac{1}{2}\leq x<2 \\ x(2x^2-11x-4)\leq 0\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} -\dfrac{1}{2}\leq x< 2 \\ \left [ \begin{matrix} 0\le x<2 \\ 2<x \le \dfrac{1}{4}(11+3\sqrt{17}) \\ x\le \dfrac{1}{4}(11-3\sqrt{17}) \end{matrix} \right. \end{array} \right.$
$\Leftrightarrow \left [ \begin{matrix} 0\le x<2 \\ -\dfrac{1}{2} \le x\le \dfrac{1}{4}(11-3\sqrt{17}) \end{matrix} \right. $