Question

why is it true when simplifying rational expressions, we must cancel factors only, and not terms

Answer 1

think of it with numbers

if you have 5 + 3 / (6 + 4) what does it come out to be? 8/10
you can simplify by reducing 8 and 10 into factors such as
2*4 / 2*5 and since 2/2 = 1 you can cancel those and then are left with 4/5

but if you write 8/10 as 5+3 / 5 +5 and try to cancel a 5 you get 3/5 which is not 4/5