a, \(A+B=5+\sqrt{15}+5-\sqrt{15}=10\)
\(AB=\left(5+\sqrt{15}\right)\left(5-\sqrt{15}\right)=5^2-\sqrt{15^2}=25-15=10\)
b, \(P=\left(\dfrac{x+3}{x-9}-\dfrac{\sqrt{x}}{\sqrt{x}+3}\right):\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)
\(\Rightarrow P=\left(\dfrac{x+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right).\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(\Rightarrow P=\left(\dfrac{x+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\dfrac{x-3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right).\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(\Rightarrow P=\dfrac{x+3-x+3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(\Rightarrow P=\dfrac{3\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\dfrac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(\Rightarrow P=\dfrac{3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)}\)
\(\Rightarrow P=\dfrac{3}{\sqrt{x}+3}\)
