Question

racionalize a expressão (x+2)/(√(x+1)+√(x+2))

Answer 1

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

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

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

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

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

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

$-(x+2).( \sqrt{x+1} - \sqrt{x+2} )$