Answer:
[tex]\large\boxed{1.\ \dfrac{1}{x}=5+2\sqrt6}\\\boxed{2.\ \dfrac{x-1}{x}=-4-2\sqrt6}\\\boxed{3.\ \dfrac{x+1}{x}=6+2\sqrt6}[/tex]
Step-by-step explanation:
[tex]x=5-2\sqrt6\\\\1.\\\\\dfrac{1}{x}=\dfrac{1}{5-2\sqrt6}=\dfrac{1}{5-2\sqrt6}\cdot\dfrac{5+2\sqrt6}{5+2\sqrt6}\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\dfrac{5+2\sqrt6}{5^2-(2\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-2^2(\sqrt6)^2}=\dfrac{5+2\sqrt6}{25-(4)(6)}=\dfrac{5+2\sqrt6}{25-24}\\\\=\dfrac{5+2\sqrt6}{1}=5+2\sqrt6\\\\2.\\\\\dfrac{x-1}{x}=\dfrac{x}{x}-\dfrac{1}{x}=1-\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x-1}{x}=1-(5+2\sqrt6)=1-5-2\sqrt6=-4-2\sqrt6[/tex]
[tex]3.\\\\\dfrac{x+1}{x}=\dfrac{x}{x}+\dfrac{1}{x}=1+\dfrac{1}{x}\\\\\text{use the value of}\ \dfrac{1}{x}\ \text{from 1.}\\\\\dfrac{x+1}{x}=1+5+2\sqrt6=6+2\sqrt6[/tex]
