Note that a factor in the numerator
can optionally be centered next to the fraction.
If everything is moved out of the
numerator, then a $\,1\,$ is inserted as a ‘placeholder’.
A factor centered next to the fraction
can be moved into the numerator.
A factor in the denominator must stay in the denominator.
are ALWAYS EQUAL.
That is, no matter what numbers are chosen for
$\,a\,,$ $\,b\,,$ and
substitution into these two expressions
yields the same number.
(Note, of course, that $\,c\,$ is not allowed
to equal zero.)
are NOT ALWAYS EQUAL.
Note that there do exist choices
for which these two expressions
give the same value:
when $\,a = 0\,,$ or
$\,b = 1\,,$ or $\,b = -1\,.$
However, for all other values of $\,b\,$
(and $\,a\ne 0\,$), they are not equal.
Assume that all variables are nonzero, so there's no concern about division by zero.