a, ĐKXĐ: \(x\ge0;x\ne1\)
\(P=\frac{x+1-2\sqrt{x}}{x+1}:\left(\frac{1}{\sqrt{x}+1}-\frac{2\sqrt{x}}{\sqrt{x}\left(x+1\right)+x+1}\right)\\=\frac{\left(\sqrt{x}-1\right)^2}{x+1}:\left(\frac{1}{\sqrt{x}+1}-\frac{2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}+1\right)}\right)\\ =\frac{\left(\sqrt{x}-1\right)^2}{x+1}:\frac{x+1-2\sqrt{x}}{\left(x+1\right)\left(\sqrt{x}+1\right)}\\ =\frac{\left(\sqrt{x}-1\right)^2}{x+1}\cdot\frac{\left(x+1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)^2}=\sqrt{x}+1\)
b, Biến đổi \(x=2019-2\sqrt{2019}+1=\left(\sqrt{2019}-1\right)^2\Rightarrow\sqrt{x}=\sqrt{2019}-1\)
Do đó với \(x=2010-2\sqrt{2019}\), ta được:
\(P=\sqrt{2019}-1+1=\sqrt{2019}\)
Chúc bạn học tốt nha
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