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ĐKXĐ: ...
\(D=\left(\frac{2\sqrt{x}}{x\left(\sqrt{x}-1\right)+\sqrt{x}-1}-\frac{1}{\sqrt{x-1}}\right):\left(\frac{x+\sqrt{x}+1}{x+1}\right)\)
\(=\left(\frac{2\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+1\right)}-\frac{x+1}{\left(\sqrt{x}-1\right)\left(x+1\right)}\right)\left(\frac{x+1}{x+\sqrt{x}+1}\right)\)
\(=\frac{\left(2\sqrt{x}-x-1\right)}{\left(\sqrt{x}-1\right)\left(x+1\right)}.\frac{\left(x+1\right)}{\left(x+\sqrt{x}+1\right)}=\frac{-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{1-\sqrt{x}}{x+\sqrt{x}+1}\)
b/ Do \(x+\sqrt{x}+1=\left(\sqrt{x}+\frac{1}{2}\right)^2+\frac{3}{4}>0\)
\(\Rightarrow\) Để \(D>0\Leftrightarrow1-\sqrt{x}>0\Leftrightarrow\sqrt{x}< 1\Rightarrow0\le x< 1\)
b: \(=\dfrac{\left|x\right|+\left|x-2\right|+1}{2x-1}=\dfrac{x+x-2+1}{2x-1}=\dfrac{2x-1}{2x-1}=1\)
c: \(=\left|x-4\right|+\left|x-6\right|\)
=x-4+6-x=2
ĐKXĐ:...
\(A=\left(\frac{\sqrt{a}+2}{\sqrt{a}\left(\sqrt{a}+2\right)}-\frac{\sqrt{a}-1}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}\right).\frac{\sqrt{a}+1}{\sqrt{a}}=\left(\frac{1}{\sqrt{a}}-\frac{1}{\sqrt{a}+1}\right).\frac{\left(\sqrt{a}+1\right)}{\sqrt{a}}\)
\(=\frac{1}{\sqrt{a}\left(\sqrt{a}+1\right)}.\frac{\left(\sqrt{a}+1\right)}{\sqrt{a}}=\frac{1}{a}\)
\(C=\left(\frac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{-\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}+\frac{\sqrt{x}\left(\sqrt{x}+1\right)\left(2\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\right).\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{2\sqrt{x}-1}\)
\(=\left(\frac{\left(\sqrt{x}+1\right)}{-\left(\sqrt{x}+1\right)}+\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{x+\sqrt{x}+1}\right).\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(2\sqrt{x}-1\right)}.\frac{\left(2\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)}\)
\(=\left(-1+\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{x+\sqrt{x}+1}\right).\sqrt{x}=\left(\frac{-x-\sqrt{x}-1+x+\sqrt{x}}{x+\sqrt{x}+1}\right)\sqrt{x}=\frac{-\sqrt{x}}{x+\sqrt{x}+1}\)
1) Khi x = 36 thì A = \(\frac{\sqrt{36}+4}{\sqrt{36}+2}\Leftrightarrow\frac{5}{4}\)
Vậy khi x = 36 thì A = \(\frac{5}{4}\)
2) B = \((\frac{\sqrt{x}\left(\sqrt{x}-4\right)}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}+\frac{4\left(\sqrt{x}+4\right)}{\left(\sqrt{x}-4\right)\left(\sqrt{x}+4\right)}):\frac{x+16}{\sqrt{x}+2}\)
= \(\frac{x-4\sqrt{x}+4\sqrt{x}+16}{x-16}.\frac{\sqrt{x}+2}{x+16}=\frac{x+16}{x-16}.\frac{\sqrt{x}+2}{x+16}\)
= \(\frac{\sqrt{x}+2}{x-16}\)
Vậy B = \(\frac{\sqrt{x}+2}{x-16}\)
