Question

Simplificando a expressão $\frac{2+ \frac{1}{ \sqrt{2} } }{ \sqrt{2}-1 }$ obtemos:
a)$\frac{11 \sqrt{2} }{2}$
b)$\frac{ \sqrt{2} }{2} + 3$
c)$\frac{7}{2} + 2 \sqrt{2}$
d)$3 + \frac{5 \sqrt{2} }{2}$
e)$\frac{2+3 \sqrt{2} }{2}$

Answer 1

vamos lá...

$\frac{2+ \frac{1}{ \sqrt{2} } }{ \sqrt{2}-1 } = \\ \\ \frac{ \frac{2 \sqrt{2} +1}{ \sqrt{2} } }{ \sqrt{2}-1 } = \\ \\ \frac{2 \sqrt{2}+1 }{ \sqrt{2} } \div \sqrt{2} -1= \\ \\ \frac{2 \sqrt{2}+1 }{ \sqrt{2} } \times \frac{1}{ \sqrt{2}-1 } = \frac{2 \sqrt{2} +1}{2- \sqrt{2} } = \\ \\ racionalizar \\ \\ \frac{(2 \sqrt{2}+1)(2+ \sqrt{2} ) }{(2- \sqrt{2})(2+ \sqrt{2} ) } = \frac{4 \sqrt{2}+4+2+ \sqrt{2} }{4-2} = \frac{6}{2} + \frac{5 \sqrt{2} }{2} =3+ \frac{5 \sqrt{2} }{2}$

R:Letra D