when you multiply anything by 1, nothing happens...so you can cancel that 1 off...
and the 1st equation doesn't equal the second...the first equation is about as simple as it gets (once you've cancelled the 1)
This is just a really unfortunate, ambiguous notation that should never have gone into use. Typically in mathematics, placing one term next to a fraction implies multiplication. But the same is occasionally done to indicate mixed fractions, hence the confusion. For clarity, you should write an explicit plus sign to indicate addition, or parentheses to indicate multiplication.
which is not, in general, equal to