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\(\sqrt{x+2\sqrt{x-2}-1}.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\sqrt{x-2+2.\sqrt{x-2}.\sqrt{1}+1}.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{x-2}-1\right)^2}.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\sqrt{x-2}-1.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\frac{\left(\sqrt{x-2}-1\right)^2}{\sqrt{x}-\sqrt{3}}\)
\(\sqrt{x+2\sqrt{x-2}-1}.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\sqrt{x+2+2.\sqrt{x-2}.\sqrt{1}-1}.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{x-2}-1\right)^2}.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\sqrt{x-2}-1.\frac{\left(\sqrt{x-2}-1\right)}{\sqrt{x}-\sqrt{3}}\)
\(=\frac{\left(\sqrt{x-2}-1\right)^2}{\sqrt{x}-\sqrt{3}}\)
Good luck !!! Rất vui vì giúp đc bạn <3
Câu 1:
Sửa đề: \(B=\left(\dfrac{x}{x+3\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right):\left(1-\dfrac{2}{\sqrt{x}}+\dfrac{6}{x+3\sqrt{x}}\right)\)
Ta có: \(B=\left(\dfrac{x}{x+3\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right):\left(1-\dfrac{2}{\sqrt{x}}+\dfrac{6}{x+3\sqrt{x}}\right)\)
\(=\left(\dfrac{x}{\sqrt{x}\left(\sqrt{x}+3\right)}+\dfrac{1}{\sqrt{x}+3}\right):\left(\dfrac{x+3\sqrt{x}-2\left(\sqrt{x}+3\right)+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}:\dfrac{x+3\sqrt{x}-2\sqrt{x}-6+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{x+\sqrt{x}}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}=1\)
Câu 3:
Ta có: \(Q=\left(\dfrac{a}{a-2\sqrt{a}}+\dfrac{a}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}+1}{a-4\sqrt{a}+4}\)
\(=\left(\dfrac{a}{\sqrt{a}\left(\sqrt{a}-2\right)}+\dfrac{a}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}+1}{\left(\sqrt{a}-2\right)^2}\)
\(=\dfrac{a+\sqrt{a}}{\sqrt{a}-2}\cdot\dfrac{\sqrt{a}-2}{\sqrt{a}+1}\cdot\dfrac{\sqrt{a}-2}{1}\)
\(=\sqrt{a}\left(\sqrt{a}-2\right)\)
\(=a-2\sqrt{a}\)
- Đề bài có SAI hoặc NHẦM gì đó nên mình sửa lại rồi chú ý gửi câu hỏi đúng lần sau bạn nhớ
Ta có : \(P=\frac{\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}}{\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}}\)
=> \(P=\frac{\sqrt{x-1+2\sqrt{x-1}+1}+\sqrt{x-1-2\sqrt{x-1}+1}}{\sqrt{x-1+2\sqrt{x-1}+1}-\sqrt{x-1-2\sqrt{x-1}+1}}\)
=> \(P=\frac{\sqrt{\left(\sqrt{x-1}+1\right)^2}+\sqrt{\left(\sqrt{x-1}-1\right)^2}}{\sqrt{\left(\sqrt{x-1}+1\right)^2}-\sqrt{\left(\sqrt{x-1}-1\right)^2}}\)
=> \(P=\frac{\sqrt{x-1}+1+\sqrt{x-1}-1}{\sqrt{x-1}+1-\sqrt{x-1}+1}\)
=> \(P=\frac{2\sqrt{x-1}}{2}=\sqrt{x-1}\)