Answer: -1/2
Step-by-step explanation:
[tex]\\\displaystyle \lim_{x \to 3} \ \dfrac{\dfrac{1}{x+5}-\dfrac{1}{8}}{\sqrt{x+1}-2} \\\\\\\displaystyle =\lim_{x \to 3} \dfrac{\dfrac{3-x}{8} }{\sqrt{x+1}-2} \\\\\\\displaystyle =\lim_{x \to 3} \dfrac{(\sqrt{x+1}+2)*\dfrac{3-x}{8} }{(\sqrt{x+1}-2)*(\sqrt{x+1}+2)} \\\\\\\displaystyle =\lim_{x \to 3} \dfrac{(\sqrt{x+1}+2)*({3-x)} }{8*(x+1-4)} \\\\\\\displaystyle =\lim_{x \to 3} \dfrac{(\sqrt{x+1}+2)*({3-x)} }{8*(x-3)} \\\\\\\displaystyle =\lim_{x \to 3} -\dfrac{ (\sqrt{x+1}+2)} {8} \\\\[/tex]
[tex]=-\dfrac{1}{2}[/tex]
