Lời giải:
\(\lim\limits_{x\to-1}\frac{x+\sqrt{4x+5}}{\sqrt{7-2x}-\sqrt{x+10}}=\lim\limits_{x\to-1}\frac{x^2-\left(4x+5\right)}{x-\sqrt{4x+5}}.\frac{\sqrt{7-2x}+\sqrt{x+10}}{7-2x-\left(x+10\right)}\)
\(=\lim\limits_{x\to-1}\frac{\left(x-5\right)\left(x+1\right)}{x-\sqrt{4x+5}}.\frac{\sqrt{7-2x}+\sqrt{x+10}}{-3\left(x+1\right)}\)
\(=\lim\limits_{x\to-1}\frac{\left(x-5\right)\left(\sqrt{7-2x}+\sqrt{x+10}\right)}{-3\left(x-\sqrt{4x+5}\right)}=\frac{\left(-1-5\right)\left(\sqrt{7-2.-1}+\sqrt{-1+10}\right)}{-3\left(-1-\sqrt{4.-1+5}\right)}=-6\)
