Question

Resta con raíces y x ​

Answer 1

Respuesta:

literal b)

Explicación paso a paso:

$\frac{ \sqrt{2} - \sqrt{x + 1} }{ \sqrt{2} + \sqrt{x + 1} }$

$= \frac{ \sqrt{2} - \sqrt{x + 1} }{ \sqrt{2} + \sqrt{x + 1} } \times \frac{ \sqrt{2} - \sqrt{x + 1} }{ \sqrt{2} - \sqrt{x + 1} }$

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

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

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

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

$= \frac{2 - 2 \sqrt{2x + 2} + x + 1}{2 - x - 1}$

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

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