Problem: For x≠0,1x+12x+13xx \neq 0, \dfrac{1}{x}+\dfrac{1}{2 x}+\dfrac{1}{3 x}xî€ =0,x1​+2x1​+3x1​ equals
Answer Choices:
A. 12x\dfrac{1}{2 x}2x1​
B. 16x\dfrac{1}{6 x}6x1​
C. 56x\dfrac{5}{6 x}6x5​
D. 116x\dfrac{11}{6 x}6x11​
E. 16x3\dfrac{1}{6 x^{3}}6x31​
Solution:
1x+12x+13x=66x+36x+26x=116x\dfrac{1}{x}+\dfrac{1}{2 x}+\dfrac{1}{3 x}=\dfrac{6}{6 x}+\dfrac{3}{6 x}+\dfrac{2}{6 x}=\dfrac{11}{6 x}x1​+2x1​+3x1​=6x6​+6x3​+6x2​=6x11​.