Answer:
[tex]\large\boxed{2.\ x=-3\ \vee\ x=3}\\\boxed{5.\ x=-\dfrac{4}{11}}\\\boxed{8.\ x=18}[/tex]
Step-by-step explanation:
[tex]2.\ Domain:\ x\neq0\\\\\dfrac{1}{x}-\dfrac{x}{9}=0\qquad\text{add}\ \dfrac{x}{9}\ \text{to both sides}\\\\\dfrac{1}{x}=\dfrac{x}{9}\qquad\text{cross multiply}\\\\(x)(x)=(1)(9)\\\\x^2=9\to x=\pm\sqrt9\\\\x=-3\ \vee\ x=3\\======================[/tex]
[tex]5.\ Domain:x\in\mathbb{R}\\\\\dfrac{3x}{4}=\dfrac{5x+1}{3}\qquad\text{cross multiply}\\\\(3x)(3)=(4)(5x+1)\qquad\text{use the distributive property}\\\\9x=(4)(5x)+(4)(1)\\\\9x=20x+4\qquad\text{subtract 20x from both sides}\\\\-11x=4\qquad\text{divide both sides by (-11)}\\\\x=-\dfrac{4}{11}\\======================[/tex]
[tex]8.\ Domain:\ x+3\neq0\to x\neq-3\\\\\dfrac{2x-1}{x+3}=\dfrac{5}{3}\qquad\text{cross multiply}\\\\3(2x-1)=5(x+3)\qquad\text{use the distributive property}\\\\(3)(2x)+(3)(-1)=(5)(x)+(5)(3)\\\\6x-3=5x+15\qquad\text{add 3 to both sides}\\\\6x=5x+18\qquad\text{subtract 5x from both sides}\\\\x=18\\======================[/tex]
