$1/\mathop {\lim }\limits_{x \to 1}\frac{\sqrt{x+3}+\sqrt{x^2+x+2}-4}{x^2-1}=\mathop {\lim }\limits_{x \to 1}\frac{\sqrt{x+3}-2}{x^2-1}+\mathop {\lim }\limits_{x \to 1}\frac{\sqrt{x^2+x+2}-2}{x^2-1}$ $=\mathop {\lim }\limits_{x \to 1}\frac{1}{(x+1)(\sqrt{x+3}+2)}+\mathop {\lim }\limits_{x \to 1}\frac{x+2}{(x+1)(\sqrt{x^2+x+2}+2)}=\frac{1}{2}$
$2/\mathop {\lim }\limits_{x \to 1}\frac{\sqrt{x+4}+\sqrt{x^2+1}-3}{x^2+x}=\frac{\sqrt{5}+\sqrt{2}-3}{2}$