a) Ta có: \(Q=\left(\dfrac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{x+1}{\sqrt{x}}-\dfrac{\sqrt{x}+1}{x-1}\right)\cdot\left(\dfrac{x+25}{x+\sqrt{x}+1}\right)\)
\(=\left(\dfrac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\left(x+1\right)\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\right)\cdot\dfrac{x+25}{x+\sqrt{x}+1}\)
\(=\dfrac{x-x\sqrt{x}+x-\sqrt{x}+1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{x+25}{x+\sqrt{x}+1}\)
\(=\dfrac{-x\sqrt{x}+2x-2\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{x+25}{x+\sqrt{x}+1}\)
\(=\dfrac{\left(\sqrt{x}-1\right)\left(-x-\sqrt{x}-1\right)+2\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{x+25}{x+\sqrt{x}+1}\)
\(=\dfrac{-x+\sqrt{x}-1}{\sqrt{x}}\cdot\dfrac{x+25}{x+\sqrt{x}+1}\)
