When subtracting 1 rational expression from another, when I'm multiplying the top & bottom of the first term by the denominator in the second term is that number automatically negative because the whole term is being subtracted?

Question

ex:
(8a-3b)/7a - (2a+5b)/4b

is the 4b negative when I multiply the first term by it?

Thanks a ton! :) ♡

Answer 1

No. However you could do it that way, but that changes the sign of the second part of the numerator, as well as the first term.
What you are fundamentally forgetting, that you are not multiplying the numerator in the first term: you are multiplying the first term by (4x/4x). Doing that makes a common denominator 28ax, and of course, you multiply the second term by (7a/7a)...

Answer 2

no
actually you are multiplying first by 4b/4b
and the second by
7a/7a
so

(4b/4b)[(8a-3b)/7a]-(7a/7a)[(2a+5b)/4b]

={4b[(8a-3b)]-7a[(2a+5b)]} /28ab

Answer 3

Ok, thank you :)