Solve for x
\left\{\begin{matrix}x\in (-\sqrt{y+1},\sqrt{y+1})\text{, }&y>-1\text{ and }y\leq 5-2\sqrt{5}\\x\in [\frac{y-3}{2},\sqrt{y+1})\text{, }&y>5-2\sqrt{5}\text{ and }y<2\sqrt{5}+5\end{matrix}\right.
Solve for y
y\in (x^{2}-1,2x+3]\text{, }x>1-\sqrt{5}\text{ and }x<\sqrt{5}+1
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