\(A=\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right):\frac{\sqrt{x}-3}{2\sqrt{x}-x}\)
a, Rút gọn
b, tìm x để A>0
c, tìm x để A=1
K
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MN
2 tháng 3 2020
Câu 3 :
\(ĐKXĐ:x>0\)
\(P=\left(\frac{2}{\sqrt{x}}+\frac{\sqrt{x}}{\sqrt{x}+2}\right):\frac{2\sqrt{x}}{x+2\sqrt{x}}\)
\(\Leftrightarrow P=\frac{2\sqrt{x}+4+x}{x+2\sqrt{x}}\cdot\frac{x+2\sqrt{x}}{2\sqrt{x}}\)
\(\Leftrightarrow P=\frac{2\sqrt{x}+4+x}{2\sqrt{x}}\)
b) Để P = 3
\(\Leftrightarrow\frac{2\sqrt{x}+4+x}{x+2\sqrt{x}}=3\)
\(\Leftrightarrow2\sqrt{x}+4+x=6\sqrt{x}\)
\(\Leftrightarrow x-4\sqrt{x}+4=0\)
\(\Leftrightarrow\left(\sqrt{x}-2\right)^2=0\)
\(\Leftrightarrow\sqrt{x}-2=0\)
\(\Leftrightarrow\sqrt{x}=2\)
\(\Leftrightarrow x=4\)(tm)
Vậy để \(P=3\Leftrightarrow x=4\)
MN
2 tháng 3 2020
Câu 1 : Hình như sai đề !! Mik sửa :
\(ĐKXĐ:\hept{\begin{cases}x\ge0\\x\ne4\end{cases}}\)
\(A=\left(\frac{x}{x\sqrt{x}-4\sqrt{x}}-\frac{6}{3\sqrt{x}-6}+\frac{1}{\sqrt{x}+2}\right):\left(\sqrt{x}-2+\frac{10-x}{\sqrt{x}+2}\right)\)
\(\Leftrightarrow A=\left(\frac{\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{2}{\sqrt{x}-2}+\frac{1}{\sqrt{x}+2}\right):\left(\frac{x-4+10-x}{\sqrt{x}+2}\right)\)
\(\Leftrightarrow A=\frac{\sqrt{x}-2\sqrt{x}-4+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}:\frac{6}{\sqrt{x}+2}\)
\(\Leftrightarrow A=\frac{-6\left(\sqrt{x}+2\right)}{6\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(\Leftrightarrow A=-\frac{1}{\sqrt{x}-2}\)
b) Để A < 2
\(\Leftrightarrow-\frac{1}{\sqrt{x}-2}< 2\)
\(\Leftrightarrow-1< 2\sqrt{x}-4\)
\(\Leftrightarrow2\sqrt{x}>3\)
\(\Leftrightarrow\sqrt{x}>1,5\)
\(\Leftrightarrow x>2,25\)
Vậy để \(A< 2\Leftrightarrow x>2,25\)
11 tháng 8 2019
các bn ơi đoạn sau mik viết nhầm đấy bỏ phần không có ngặc đi nha
MN
10 tháng 7 2020
a) \(A=\left(\frac{4\sqrt{x}}{\sqrt{x}+2}-\frac{8x}{x-4}\right):\left(\frac{\sqrt{x}-1}{x-2\sqrt{x}}-\frac{2}{\sqrt{x}}\right)\)
\(\Leftrightarrow A=\frac{4\sqrt{x}\left(\sqrt{x}-2\right)-8x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}:\frac{\sqrt{x}-1-2\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(\Leftrightarrow A=\frac{4x-8\sqrt{x}-8x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}:\frac{\sqrt{x}-1-2\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(\Leftrightarrow A=\frac{-4x-8\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}:\frac{-\sqrt{x}+3}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(\Leftrightarrow A=\frac{-4\sqrt{x}}{\sqrt{x}-2}\cdot\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{-\sqrt{x}+3}\)
\(\Leftrightarrow A=\frac{4x}{\sqrt{x}-3}\)
b) Để \(A=-1\)
\(\Leftrightarrow\frac{4x}{\sqrt{x}-3}=-1\)
\(\Leftrightarrow4x=3-\sqrt{x}\)
\(\Leftrightarrow4x+\sqrt{x}-3=0\)
\(\Leftrightarrow\left(\sqrt{x}+1\right)\left(4\sqrt{x}-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x}+1=0\\4\sqrt{x}-3=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x}=-1\left(ktm\right)\\\sqrt{x}=\frac{3}{4}\Leftrightarrow x=\frac{9}{16}\left(tm\right)\end{cases}}\)
Vậy để \(A=-1\Leftrightarrow x=\frac{9}{16}\)
c) Khi \(x=36\)
\(\Leftrightarrow A=\frac{4\cdot36}{\sqrt{36}-3}=\frac{144}{3}=48\)
Q
23 tháng 11 2019
a) \(A=\left(\frac{4\sqrt{x}}{\sqrt{x}+2}-\frac{8x}{x-4}\right):\left(\frac{\sqrt{x}-1}{\left(x-2\sqrt{x}\right)}-\frac{2}{\sqrt{x}}\right)\)
\(A=\left(\frac{4\sqrt{x}}{\sqrt{x}+2}-\frac{8x}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right):\left(\frac{\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-2\right)}-\frac{2}{\sqrt{x}}\right)\)
\(A=\left(\frac{4\sqrt{x}\left(\sqrt{x}-2\right)-8x}{\left(\sqrt{x}+2\right)\left(x-2\right)}\right):\left(\frac{\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)
\(A=\left(\frac{4x-8\sqrt{x}-8x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}\right)}\right):\left(\frac{\sqrt{x}-1-2\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)
\(A=\left(\frac{-8\sqrt{x}-4x}{\left(\sqrt{x}+2\right)\sqrt{x}}\right):\left(\frac{3-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}\right)\)
\(A=\left(\frac{-4\sqrt{x}\left(2-\sqrt{x}\right)}{\left(\sqrt{x}+2\right)\sqrt{x}}\right).\left(\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{3-\sqrt{x}}\right)\)
\(A=\frac{-4\sqrt{x}\left(2-\sqrt{x}\right).\sqrt{x}\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}+2\right)\left(3-\sqrt{x}\right)}\)
\(A=\frac{-4\sqrt{x}\left(2-\sqrt{x}\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(3-\sqrt{x}\right)}\)
.......... Đến đây bạn tự nhân đa thức với đa thức xog rút gọn nha.
a)\(A=\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}-\frac{4x}{x-4}\right):\frac{\sqrt{x}-3}{2\sqrt{x}-x}\)
\(A=\left(\frac{2+\sqrt{x}}{2-\sqrt{x}}-\frac{2-\sqrt{x}}{2+\sqrt{x}}+\frac{4x}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}\right).\frac{\sqrt{x}\left(2-\sqrt{x}\right)}{\sqrt{x}-3}\)
\(A=\frac{\left(2+\sqrt{x}\right)^2-\left(2-\sqrt{x}\right)^2+4x}{\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)}.\frac{\sqrt{x}\left(2-\sqrt{x}\right)}{\sqrt{x}-3}\)
\(A=\frac{x+4\sqrt{x}+4-\left(x-4\sqrt{x}+4\right)+4x}{2+\sqrt{x}}.\frac{\sqrt{x}}{\sqrt{x}-3}\)
\(A=\frac{x+4\sqrt{x}+4-x+4\sqrt{x}-4+4x}{2+\sqrt{x}}.\frac{\sqrt{x}}{\sqrt{x}-3}\)
\(A=\frac{8\sqrt{x}+4x}{2+\sqrt{x}}.\frac{\sqrt{x}}{\sqrt{x}-3}\)
\(A=\frac{4\sqrt{x}(2+\sqrt{x})}{2+\sqrt{x}}.\frac{\sqrt{x}}{\sqrt{x}-3}\)
\(A=\frac{4x}{\sqrt{x}-3}\)
đk: \(x\ne4;x\ne9;x\ge0\)
\(A>0\)\(=>A=\frac{4x}{\sqrt{x}-3}>0\)
có \(x\ge0=>4x\ge0\)
\(=>A>0=>\sqrt{x}-3>0< =>\sqrt{x}>3< =>x>9\)
vậy x>9 thì A>0