a.
\(A=\dfrac{x-y+10y+6\sqrt{xy}}{\sqrt{x}+3\sqrt{y}}=\dfrac{x+6\sqrt{xy}+9y}{\sqrt{x}+3\sqrt{y}}\)
\(=\dfrac{\left(\sqrt{x}+3\sqrt{y}\right)^2}{\sqrt{x}+3\sqrt{y}}=\sqrt{x}+3\sqrt{y}\)
b.
ĐKXĐ: \(x\ge5\)
\(\dfrac{\sqrt{x-5}}{\sqrt{x}-2}=2\Rightarrow\sqrt{x-5}=2\sqrt{x}-4\)
\(\Leftrightarrow\sqrt{x-5}+4=2\sqrt{x}\)
\(\Leftrightarrow x-5+16+8\sqrt{x-5}=4x\)
\(\Leftrightarrow8\sqrt{x-5}=3x-11\)
\(\Rightarrow64\left(x-5\right)=\left(3x-11\right)^2\)
\(\Leftrightarrow9x^2-130x+441=0\Rightarrow\left[{}\begin{matrix}x=9\\x=\dfrac{49}{9}\end{matrix}\right.\) (thỏa mãn)
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