Question

Racionalize os denominadores, calcule e simplifique:

Answer 1

$\dfrac{2 + \sqrt{2}}{ \sqrt{2} - 1} - \dfrac{6}{ \sqrt{2}} \\ \\ \\ \sqrt{2} (3 + 2 \sqrt{2} ) - 3 \sqrt{2} \\ \\ \\ 4 + 3 \sqrt{2} - 3 \sqrt{2} \\ \\ => \fbox{ \ \ 4\ \ }$

Answer 2

vamos racionalizar

$\frac{2+ \sqrt{2} }{ \sqrt{2}-1 } = \frac{(2+ \sqrt{2})( \sqrt{2} +1) }{( \sqrt{2-1)( \sqrt{2} +1)} } =$

$\frac{2 \sqrt{2}+2+ \sqrt{2^2} + \sqrt{2} }{ \sqrt{2^2}-1^2 } = \frac{3 \sqrt{2}+2+2 }{2-1} =$

$\fbox{ 3 \sqrt{2} +4 }$

agora

$\frac{6}{ \sqrt{2} } = \frac{6. \sqrt{2} }{ \sqrt{2}. \sqrt{2} } = \frac{6 \sqrt{2} }{ \sqrt{2^2} } = \frac{6 \sqrt{2} }{2} =[tex]\fbox{ 3 \sqrt{2} }$

vamos calcular

$3 \sqrt{2} +4-3 \sqrt{2} =\fbox{ 4 }$