Đáp án:
Giải thích các bước giải:
$y=\dfrac{x-1 + 3\sqrt[]{x-1} +2}{x-1 +4\sqrt[]{x-1} +3}\\
=\dfrac{(\sqrt[]{x-1}+1)(\sqrt[]{x-1}+2)}{(\sqrt[]{x-1}+1)(\sqrt[]{x-1}+3)}\\
=\dfrac{(\sqrt[]{x-1}+2)}{(\sqrt[]{x-1}+3)}\\
=1-\dfrac{1}{(\sqrt[]{x-1}+3}\\
\geq 1 -\dfrac{1}{0+3}=\dfrac{2}{3}$