Bạn tham khảo:
a/ĐKXĐ:x>0,x khác 1
$P=(\dfrac{1}{\sqrt{x}-1}-$ $\dfrac{2\sqrt{x}}{(x+1)(\sqrt{x}-1)}):$$(\dfrac{\sqrt{x}(\sqrt{x}+1)}{(x+1)(\sqrt{x}+1)})$
$P=\dfrac{x+1-2\sqrt{x}}{(x+1).(\sqrt{x}-1)}:$ $\dfrac{\sqrt{x}}{x+1}$
$P=\dfrac{(\sqrt{x}-1)^2}{(x+1)(\sqrt{x}-1)}.$ $\dfrac{x+1}{\sqrt{x}}$
$P=\dfrac{\sqrt{x}-1}{\sqrt{x}}$
b/ $P=\sqrt{x}-2$
⇔$\dfrac{\sqrt{x}-1}{x}=\sqrt{x}-2$
⇔$\sqrt{x}-1=x-2\sqrt{x}$
⇔$x-3\sqrt{x}+1=0$
$Δ=9-4=5$
Vì $Δ>0$ nên phương trình có 2 nghiệm
$x_{1}=$ $\dfrac{3+\sqrt{5}}{1}=3+\sqrt{5}$
$x_{2}=3-\sqrt{5}$
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