$12.3 \lim _{x \rightarrow-1} \frac{\sqrt{2 x+3}-1}{\sqrt{5+x}-2}$.

$12.3 \lim _{x \rightarrow-1} \frac{\sqrt{2 x+3}-1}{\sqrt{5+x}-2}$. 

The above text is already in a mathematical expression format, so the translation is the same as the original text. If you need an explanation or solution for the limit, please let me know!
12.3 Multiplying the numerator and the denominator of the fraction by $(\sqrt{2 x+3}+1)(\sqrt{5+x}+2)$, we get $\lim _{x \rightarrow-1} \frac{(2 x+3-1)(\sqrt{5+x}+2)}{(5+x-4)(\sqrt{2 x+3}+1)}=\lim _{x \rightarrow-1} \frac{2(x+1)(\sqrt{5+x}+2)}{(x+1)(\sqrt{2 x+3}+1)}=$ $\lim _{x \rightarrow-1} \frac{2(\sqrt{5+x}+2)}{\sqrt{2 x+3}+1}=\frac{2 \cdot 4}{2}=4$.

Answer: 4.