Provide them with concrete examples, using real numbers (not Real as in the complete ordered field, but "real" as in quantitative).

Next time a student thinks that they can use $$\frac{a}{b+c} "=" \frac{a}{b}+\frac{a}{c}$$ give them an easy problem to check: does $\frac{12}{2+4} = \frac{12}{2}+\frac{12}{4}$? No, so the property must not hold.

The problem most (middle and high school) students have is that they can't yet deal with variables in the same way as numbers. They think it's a whole different world; it's too abstract. So give them problems they can understand, with actual numbers. Then they'll begin to notice patterns, which will lead to the abstract.