\(1,P=\dfrac{2\sqrt{x}}{\sqrt{x}+3}\cdot\dfrac{\sqrt{x}+3}{\sqrt{x}+2}+\dfrac{9\sqrt{x}+14}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\\ P=\dfrac{2\sqrt{x}}{\sqrt{x}+2}+\dfrac{9\sqrt{x}+14}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\\ P=\dfrac{2x+2\sqrt{x}+9\sqrt{x}+14}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}\\ P=\dfrac{2x+11\sqrt{x}+14}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}=\dfrac{\left(\sqrt{x}+2\right)\left(2\sqrt{x}+7\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}=\dfrac{2\sqrt{x}+7}{\sqrt{x}+1}\)
\(2,x=4\Leftrightarrow P=\dfrac{2\cdot2+7}{2+1}=\dfrac{11}{3}\)
\(3,P=\dfrac{2\left(\sqrt{x}+1\right)+5}{\sqrt{x}+1}=2+\dfrac{5}{\sqrt{x}+1}\in N\\ \Leftrightarrow\sqrt{x}+1\inƯ\left(5\right)=\left\{1;5\right\}\\ \Leftrightarrow\sqrt{x}\in\left\{0;4\right\}\\ \Leftrightarrow x\in\left\{0;16\right\}\left(tm\right)\)
