Quick question on how much to simplify

[Mercury3190]

The equation is: 9 over [5 + (square root of 3).
Is the correct simplified answer [45 - 9*(square root of 3)] over 22 ... or ... [9*[5 - (square root of 3)]] all over 22? --> they are the same numerically.
Should the 9 be brought outside the equation on top (becuase it goes into 45), or left inside?
I appreciate your help.

 

[stapel]

You have an unpaired grouping symbol in your post...?

I think you mean the following:


. . . . .\(\displaystyle \large{\frac{9}{5\,+\,\sqrt{3}}}\)


If so, then, to simplify, multiply top and bottom by the conjugate, 5 - sqrt[3].

Most books, I think, would expect the "simplified" answer not to have any parentheses in it, so you'd likely need to multiply things out. But "simplify" does not, unfortunately, have a fixed meaning, so you'll need to look at your class notes and/or at worked examples from the text to discern the precise expectations in your particular case.

Eliz.