đkxđ: x≠9
\(P=\left(\dfrac{\sqrt{x}+3}{\sqrt{x}+2}+\dfrac{4x\sqrt{x}+3x+9}{x-\sqrt{x}-6}\right):\left(\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{2\sqrt{x}+3}{x+5\sqrt{x}+6}\right)\)
\(=\left[\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}+\dfrac{4x\sqrt{x}+3x+9}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\right]:\left[\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+2\right)}+\dfrac{2\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+2\right)}\right]\)
\(=\dfrac{x-9+4x\sqrt{x}+3x+9}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}:\dfrac{x+2\sqrt{x}+2\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+2\right)}\)
\(=\dfrac{4x\sqrt{x}+4x}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\cdot\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{4x\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}=\dfrac{4x}{\sqrt{x}-3}\)
b/ \(P=48\Leftrightarrow\dfrac{4x}{\sqrt{x}-3}=48\)
\(\Leftrightarrow4x=48\sqrt{x}-144\)
\(\Leftrightarrow4x-48\sqrt{x}+144=0\)
\(\Leftrightarrow\left(2\sqrt{x}-12\right)^2=0\)
\(\Leftrightarrow2\sqrt{x}-12=0\Leftrightarrow\sqrt{x}=6\Leftrightarrow x=36\)(TM)
Vậy................
