Rút gọn F biết F = ( \(\sqrt{x}\) - \(\frac{1}{\sqrt{x}}\)).(\(\frac{\sqrt{x}}{\sqrt{x+}1}\)+ \(\frac{\sqrt{x}}{\sqrt{x}-1}\))
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a, ĐKXĐ : x > 0 và x khác 9
F = x-\(3\sqrt{x}\)+x+\(3\sqrt{x}\)/x-9 . x-9/\(\sqrt{x}\)
= 2x/x-9 . x-9/\(\sqrt{x}\) = 2x\(\sqrt{x}\)
b, F = 1/2 <=> 2x\(\sqrt{x}\)=1/2
<=>x\(\sqrt{x}\) = 1/4 hay \(\sqrt{x}^3\) = 1/4
<=> \(\sqrt{x}=\sqrt[3]{\frac{1}{4}}\)
<=> x=\(\sqrt[3]{\frac{1}{4}}^2\)
Nếu đúng thì k mk nha
a, \(\left(\frac{1}{x+2\sqrt{x}}-\frac{1}{\sqrt{x}+2}\right):\frac{1-\sqrt{x}}{x+4\sqrt{x}+4}\)ĐK : x >= 0 ; \(x\ne1\)
\(=\left(\frac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\right).\frac{\left(\sqrt{x}+2\right)^2}{1-\sqrt{x}}=\frac{\sqrt{x}+2}{\sqrt{x}}\)
b, \(F=\frac{5}{2}\Rightarrow\frac{\sqrt{x}+2}{\sqrt{x}}=\frac{5}{2}\Rightarrow2\sqrt{x}+4=5\sqrt{x}\Leftrightarrow3\sqrt{x}=4\Leftrightarrow x=\frac{16}{9}\)
ĐK : x > 0 , x khác 1
\(bthuc=\frac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\frac{\left(\sqrt{x}+2\right)^2}{1-\sqrt{x}}=\frac{\sqrt{x}+2}{\sqrt{x}}\)
Để bthuc = 5/2 thì \(\frac{\sqrt{x}+2}{\sqrt{x}}=\frac{5}{2}\Rightarrow2\sqrt{x}+4=5\sqrt{x}\Leftrightarrow3\sqrt{x}=4\Leftrightarrow x=\frac{16}{9}\left(tm\right)\)
\(P=\dfrac{x+\sqrt{x}+1-x+\sqrt{x}-1}{\sqrt{x}}+\dfrac{x-1}{\sqrt{x}}\cdot\dfrac{x+2\sqrt{x}+1+x-2\sqrt{x}+1}{x-1}\)
\(=2+\dfrac{2x+2}{\sqrt{x}}=\dfrac{2x+2\sqrt{x}+2}{\sqrt{x}}\)
\(\dfrac{2\sqrt{x}}{\sqrt{x}-2}-\dfrac{5\sqrt{x}-2}{x-2\sqrt{x}}-\dfrac{\sqrt{x}+1}{\sqrt{x}}\left(x>0;x\ne4\right)\)
\(=\dfrac{2\sqrt{x}}{\sqrt{x}-2}-\dfrac{5\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}-2\right)}-\dfrac{\sqrt{x}+1}{\sqrt{x}}\)
\(=\dfrac{2\sqrt{x}\cdot\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}-\dfrac{5\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}-2\right)}-\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{2x-5\sqrt{x}+2-x+\sqrt{x}+2}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{x-4\sqrt{x}+4}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\dfrac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(A=\dfrac{\sqrt{x}-2}{\sqrt{x}}\)