Question

X-1/raiz(x+3)-1 como racionalizar.

Answer 1

$\textrm{Racionalizaremos a express\~ao multiplicando-a}\\ \textrm{pelo conjugado do denominador:}\\\\ \mathrm{\dfrac{x-1}{\sqrt{x+3}-1}=\dfrac{x-1}{\sqrt{x+3}-1}\times\dfrac{\sqrt{x+3}+1}{\sqrt{x+3}+1}=}\\\\\\ \mathrm{\dfrac{x\sqrt{x+3}+x-\sqrt{x+3}-1}{x+3+\sqrt{x+3}-\sqrt{x+3}-1}=\dfrac{(x-1)\sqrt{x+3}+x-1}{x+2}}$