$$\frac{x+2}{4x\:}=\frac{3x-1}{3x}$$
Putting this code into Cymath, the first step is: "Cancel x on both sides." Then "Multiply both sides by 12 (the LCM of 4, 3)."
How was that possible? What method or teaching did they use to be able to do it and how was it done?
I tried the equation in Symbol and Quickmath and both have steps that do:
$$3x(x + 2) = 4x(3x - 1)$$
Wouldn't I do $3x * x = 3x^2$? The solutions show, it is just $3x$. So what happened to the $x$?
You don't have to multiply both sides by $3x$ and $4x$ as Symbol and Quickmath do. It's enough to multiply both sides by $3, 4$ and $x$, and simplify the resulting fractions. That way, you get $$ 3(x+2)=4(3x-1) $$ Cymath seems to treat "multiply both sides by $x$" and "multiply both sides by $12$" as two completely different kinds of operations, which, to be fair, is probably necessary in a computer program. We humans, however, can treat the two as basically the same.
Just remember that multiplying by something with $x$ might introduce extra solutions into our equation. For instance, Symbol's and Quickmath's multiplication by $3x\cdot 4x=12x^2$ gives us an equation where $x=0$ is a solution, even though that's not a solution to the original equation.
PS: Note that strictly speaking, using the formal, rigorous, conventional definition of fractions, the expression $$ \frac{x+2}{4x}=\frac{3x-1}{3x} $$ truly means $$ 3x(x+2)=4x(3x-1) $$ (as long as the denominators aren't $0$). So calling that step of going from the top one to the bottom one "multiply on both sides" is imprecise. The step is actually called "apply the definition of fractions".