\(A=\dfrac{3x+4\sqrt{x}-7}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}+\dfrac{1-x}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}-\dfrac{x-\sqrt{x}-6}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}\)
\(=\dfrac{3x+4\sqrt{x}-7+1-x-x+\sqrt{x}+6}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x+5\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)