3: \(A=\dfrac{10\sqrt{x}}{x+3\sqrt{x}-4}-\dfrac{2\sqrt{x}-3}{\sqrt{x}+4}+\dfrac{\sqrt{x}+1}{1-\sqrt{x}}\)
\(=\dfrac{10\sqrt{x}}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}-\dfrac{2\sqrt{x}-3}{\sqrt{x}+4}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(=\dfrac{10\sqrt{x}-\left(2\sqrt{x}-3\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}+1\right)\left(\sqrt{x}+4\right)}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{10\sqrt{x}-\left(2x-5\sqrt{x}+3\right)-\left(x+5\sqrt{x}+4\right)}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{10\sqrt{x}-2x+5\sqrt{x}-3-x-5\sqrt{x}-4}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-3x+10\sqrt{x}-7}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{-\left(3\sqrt{x}-7\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+4\right)\left(\sqrt{x}-1\right)}=\dfrac{-3\sqrt{x}+7}{\sqrt{x}+4}\)
4: \(A=\left(\dfrac{4x}{4-x}+\dfrac{2+\sqrt{x}}{2-\sqrt{x}}-\dfrac{2-\sqrt{x}}{2+\sqrt{x}}\right):\dfrac{\sqrt{x}+3}{2-\sqrt{x}}\)
\(=\left(\dfrac{4x}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}+\dfrac{2+\sqrt{x}}{2-\sqrt{x}}-\dfrac{2-\sqrt{x}}{\left(2+\sqrt{x}\right)}\right)\cdot\dfrac{2-\sqrt{x}}{\sqrt{x}+3}\)
\(=\dfrac{4x+\left(2+\sqrt{x}\right)^2-\left(2-\sqrt{x}\right)^2}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}\cdot\dfrac{2-\sqrt{x}}{\sqrt{x}+3}\)
\(=\dfrac{4x+x+4\sqrt{x}+4-\left(x-4\sqrt{x}+4\right)}{2+\sqrt{x}}\cdot\dfrac{1}{\sqrt{x}+3}\)
\(=\dfrac{5x+4\sqrt{x}+4-x+4\sqrt{x}-4}{\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)}\)
\(=\dfrac{4x+8\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)}=\dfrac{4\sqrt{x}\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\cdot\left(\sqrt{x}+3\right)}=\dfrac{4\sqrt{x}}{\sqrt{x}+3}\)
5: \(A=\left(\dfrac{x+2\sqrt{x}}{x-2\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)\cdot\dfrac{1}{\sqrt{x}+1}\)
\(=\left(\dfrac{\sqrt{x}+2}{\sqrt{x}-2}+\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)\cdot\dfrac{1}{\sqrt{x}+1}\)
\(=\dfrac{2\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{2\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)}=\dfrac{2}{\sqrt{x}-2}\)
