For $x \in \mathbb{R}$,the minimum value of $\frac{x^2+2x+5}{x^2+4x+10}$ is

The values of $\frac{x^2-2x+1}{x^2+x-1}$ do not lie in the interval

$\sqrt{x + 2\sqrt{x - 1}} + \sqrt{x - 2\sqrt{x - 1}} = $

For $0 < c < b < a$,let $(a+b-2c)x^2 + (b+c-2a)x + (c+a-2b) = 0$ and $\alpha \neq 1$ be one of its roots. Then,among the two statements:
$(I)$ If $\alpha \in (-1, 0)$,then $b$ cannot be the geometric mean of $a$ and $c$.
$(II)$ If $\alpha \in (0, 1)$,then $b$ may be the geometric mean of $a$ and $c$.

If $\frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2$ for all $x \in R$,then $a=$

If $x$ is real,the expression $\frac{x + 2}{2x^2 + 3x + 6}$ takes all values in the interval