Answer:
x is any real number except 0.
Step-by-step explanation:
[tex]\text{Domain}:\ x\neq0[/tex]
[tex]\dfrac{1}{x}-\dfrac{1}{3x}=\dfrac{1}{2x}+\dfrac{1}{6x}\qquad\text{multiply both sides by 6}\\\\6\cdot\dfrac{1}{x}-6\!\!\!\!\diagup^2\cdot\dfrac{1}{\not3_1x}=6\!\!\!\!\diagup^3\cdot\dfrac{1}{\not2_1x}+6\!\!\!\!\diagup^1\cdot\dfrac{1}{\not6_1x}\\\\\dfrac{6}{x}-\dfrac{2}{x}=\dfrac{3}{x}+\dfrac{1}{x}\qquad\text{subtract}\ \dfrac{3}{x}\ \text{and}\ \dfrac{1}{x}\ \text{from both sides}\\\\\dfrac{6}{x}-\dfrac{2}{x}-\dfrac{3}{x}-\dfrac{1}{x}=0\\\\\dfrac{6-2-3-1}{x}=0\\\\\dfrac{0}{x}=0\\\\0=0\ TRUE[/tex]
