a: Ta có: \(A=\dfrac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\dfrac{3\sqrt{x}-2}{\sqrt{x}-1}-\dfrac{3}{\sqrt{x}+3}\)
\(=\dfrac{15\sqrt{x}-11-3x-9\sqrt{x}+2\sqrt{x}+6-3\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-3x+5\sqrt{x}-2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-3\sqrt{x}+2}{\sqrt{x}+3}\)
b: Để A nguyên thì \(-3\sqrt{x}+2⋮\sqrt{x}+3\)
\(\Leftrightarrow11⋮\sqrt{x}+3\)
\(\Leftrightarrow\sqrt{x}+3=11\)
hay x=64
c: Thay \(x=3-2\sqrt{2}\) vào A, ta được:
\(A=\dfrac{-3\left(\sqrt{2}-1\right)+2}{\sqrt{2}-1+3}=\dfrac{5-3\sqrt{2}}{2+\sqrt{2}}=\dfrac{16-11\sqrt{2}}{2}\)
