Respostas

  • Usuário do Brainly
2013-05-27T20:47:02-03:00

Primeiramente, observe que

 

\text{mmc}(\sqrt{3}-1, \sqrt{3}, 1+\sqrt{3})=\sqrt{3}\cdot(\sqrt{3}-1)\cdot(\sqrt{3}+1)

 

Desta maneira, temos:

 

\dfrac{\sqrt{3}\cdot\sqrt{3}\cdot(1+\sqrt{3})-1\cdot(\sqrt{3}-1)\cdot(1+\sqrt{3})+2\cdot(\sqrt{3}-1)\cdot\sqrt{3}}{\sqrt{3}\cdot(\sqrt{3}-1)\cdot(\sqrt{3}+1)}

 

=\dfrac{3+3\sqrt{3}+1+6+2\sqrt{3}}{\sqrt{3}\cdot(\sqrt{3}-1)\cdot(\sqrt{3}+1)}

 

=\dfrac{10+5\sqrt{3}}{\sqrt{3}}=\dfrac{10\sqrt{3}}{3}+5