Simplest form of a fraction

[Nazariy]

Hello, how come the following

$\displaystyle \dfrac{3\, +\, \sqrt{3\,}}{1\, +\, \sqrt{3\,}}$

is equal to square root of three? Thank you.

 

[lookagain]

I would have tried multiplying the numerator and the denominator by
the conjugate of the denominator.


But do this instead for less work. Factor out a square root of three in
the numerator and see what you can cancel.


$\displaystyle \dfrac{3 \ + \ \sqrt{3}}{1 \ + \ \sqrt{3}} \ =$



$\displaystyle \dfrac{\sqrt{3}( \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ )}{ \ \ \ \ \ 1 \ + \ \sqrt{3}} \ = \ ?$

 

[Nazariy]

I would have tried multiplying the numerator and the denominator by
the conjugate of the denominator.


But do this instead for less work. Factor out a square root of three in
the numerator and see what you can cancel.


$\displaystyle \dfrac{3 \ + \ \sqrt{3}}{1 \ + \ \sqrt{3}} \ =$



$\displaystyle \dfrac{\sqrt{3}( \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ )}{ \ \ \ \ \ 1 \ + \ \sqrt{3}} \ = \ ?$

ahhh! smart. thanks