Đáp án:
$\dfrac{-9+\sqrt[]{5}}{19}$
Giải thích các bước giải:
$C=\dfrac{\sqrt[]{x}-1}{x+\sqrt[]{x}+1}=$ $\dfrac{\sqrt[]{x}-1}{(\sqrt[]{x})^2-2.\dfrac{1}{2}\sqrt[]{x}+\bigg(\dfrac{1}{2}\bigg)^2+\dfrac{3}{4}}$
$=$$\dfrac{\sqrt[]{x}-1}{(\sqrt[]{x}+\dfrac{1}{2})^2+\dfrac{3}{4}}$
$x=9-4\sqrt[]{5}=(\sqrt[]{5}-2)^2$
$\sqrt[]{x}=\sqrt[]{(\sqrt[]{5}-2)^2}=|\sqrt[]{5}-2|=\sqrt[]{5}-2$
$C=\dfrac{\sqrt[]{5}-2-1}{[(\sqrt[]{5}-2)+\dfrac{1}{2}]^2+\dfrac{3}{4}}=$ $\dfrac{-9+\sqrt[]{5}}{19}$
