What are the solutions of $|x+y|=|x|+|y|$? So I am having a problem in solving this type of equation. 
The problem I am dealing with is...
$$\left|(2x-1) + \frac{3x-1}x\right| = \left|2x-1\right| + \left|\frac{3x-1}x\right|$$
Please help me with this problem. 
Thank you so much. 

Hint: If considered over the reals, $|a+b| = |a| + |b|$ holds if and only if $a$ and $b$ are of same sign, or at least one of $a, b$ is $0$.
For you question, determine the intervals over which $2x-1$ is positive/zero/negative, and the intervals over which $(3x-1)/x$ is positive/zero/negative, and then take suitable unions/intersections. (Care must be taken at then endpoint $x = 0$, since $x$ appears in denominators.)
