Simplifying surds as numerators

[MattVonFat]

Hi,

I was reading about surds and saw this:

[PLAIN]http://www.mattvonfat.com/eq.png

I'm probably not as familiar with simplifying fractions as I should be but I think I get that it's being split into two fractions and that √3/2 is the same as 1/2*√3 but I don't understand what's actually being done to √3/2 to simplify it and why the original expression isn't left as it is.

Any help would be much appreciated!

Thanks,
Matt

 

[paulfr]

Nothing wrong with either form of the expression.
Usually we eliminate roots from denominators.
Numerators with roots are fine.

 

[cone]

it might help to think of it like this:

2/3 - 1/3 = (2-1)/3

So reverse would be the same:

(2-1)/3 = 2/3 - 1/3

if 3 were negative, then the negatives would evaluate:

(2-1)/-3 = 2/-3 - 1/-3 = -2/3 - (-1/3) = -2/3 + 1/3