Question

How do i solve 1/x-1/3x=1/2x+1/6x

Answer 1

x is any real number except 0.

Explanation:

`\text{Domain}:\ x\\eq0`

`(1)/(x)-(1)/(3x)=(1)/(2x)+(1)/(6x)\qquad\text{multiply both sides by 6}\\\\6\cdot(1)/(x)-6\!\!\!\!\diagup^2\cdot(1)/(\\ot3_1x)=6\!\!\!\!\diagup^3\cdot(1)/(\\ot2_1x)+6\!\!\!\!\diagup^1\cdot(1)/(\\ot6_1x)\\\\(6)/(x)-(2)/(x)=(3)/(x)+(1)/(x)\qquad\text{subtract}\ (3)/(x)\ \text{and}\ (1)/(x)\ \text{from both sides}\\\\(6)/(x)-(2)/(x)-(3)/(x)-(1)/(x)=0\\\\(6-2-3-1)/(x)=0\\\\(0)/(x)=0\\\\0=0\ TRUE`