Nested Fractions Help

CluelessCarl

New member
Joined
Nov 12, 2014
Messages
2
Hey. I have a question, and I'd appreciate it if somebody could help out.

Basically, I have been doing nested fractions with variables in them and have been getting along fine, but in a few cases when I simplify, I take it too far and get the answer wrong.

For example:
One answer was:
y + 1
----------
y + 3

But I just wrote 1/3

Another answer was:
3x^2
---------
4x+6

But I wrote:
3x
------
4+6

So I try to cancel out the variables but it turns out wrong. Other times when I cancel out the variables it turns out right. Does anyone know what I am doing wrong or what rule I'm breaking so that I don't keep making the same mistake?
 
Surely you know from arithmetic that \(\displaystyle \frac{3}{4}= \frac{2+ 1}{2+ 2}\) is NOT equal to \(\displaystyle \frac{1}{2}\). A fraction is an "indicated division". Division, like multiplication, simply does NOT "play well" with addition and subtraction! You can only cancel factors- numbers, or algebraic quantities, that are multiplied in the numerator and denominator, not added or subtracted.
 
Thanks a lot guys. This makes things a lot clearer. I knew it was kind of a silly question and I was obviously operating under some wrong preconception. But it's something I've had a bit of trouble with for quite some time, so its good to finally put it to rest. :)
 
Top