1: \(P=\dfrac{a+6\sqrt{a}+9}{\sqrt{a}+3}+\dfrac{a-9}{\sqrt{a}-3}\)
\(=\dfrac{\left(\sqrt{a}+3\right)^2}{\sqrt{a}+3}+\dfrac{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}{\sqrt{a}-3}\)
\(=\sqrt{a}+3+\sqrt{a}+3=2\sqrt{a}+6\)
2: Thay \(a=19-6\sqrt{10}=\left(\sqrt{10}-3\right)^2\) vào P, ta được:
\(P=2\cdot\sqrt{\left(\sqrt{10}-3\right)^2}+6\)
\(=2\left(\sqrt{10}-3\right)+6=2\sqrt{10}-6+6=2\sqrt{10}\)
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