Simplest form of a fraction

Nazariy

Junior Member
Joined
Jan 21, 2014
Messages
124
Hello, how come the following

\(\displaystyle \dfrac{3\, +\, \sqrt{3\,}}{1\, +\, \sqrt{3\,}}\)

is equal to square root of three? Thank you.
 
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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.


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



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