\(A=\dfrac{7\sqrt{x}+3}{9-x}+\dfrac{2\sqrt{x}}{\sqrt{x}+3}+\dfrac{\sqrt{x}+1}{\sqrt{x}-3}=\dfrac{7\sqrt{x}+3}{9-x}+\dfrac{2\sqrt{x}}{\sqrt{x}+3}-\dfrac{\sqrt{x}+1}{3-\sqrt{x}}=\dfrac{7\sqrt{x}+3}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}+\dfrac{2\sqrt{x}\left(3-\sqrt{x}\right)}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}-\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}=\dfrac{7\sqrt{x}+3}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}+\dfrac{6\sqrt{x}-2x}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}-\dfrac{x+4\sqrt{x}+3}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}=\dfrac{7\sqrt{x}+3+6\sqrt{x}-2x-x-4\sqrt{x}-3}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}=\dfrac{9\sqrt{x}-3x}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}=\dfrac{3\sqrt{x}\left(3-\sqrt{x}\right)}{\left(3-\sqrt{x}\right)\left(3+\sqrt{x}\right)}=\dfrac{3\sqrt{x}}{\sqrt{x}+3}\)
