In the examples you cited, "numerators" are subject to "linearity" but "denominators" are not.

For instance, $$ \frac{a+b}{c} \mathrel{\text{“=”}} \frac{a}{c} + \frac{b}{c} $$

is true, but $$ \frac{1}{a+b} \mathrel{\text{“=”}} \frac{1}{a} + \frac{1}{b} $$ is not.

And $$ 2^{-3} \mathrel{\text{“=”}} 1/2^3 $$, meaning that once you put $$ 2^{3} $$ in the denominator, the linear relationship breaks down.

Once I learned that expressions are linear in numerators but not in denominators, it was a big step forward for me.