1.1) \(\left\{{}\begin{matrix}2x-3y=-7\\4x+y=-7\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}4x-6y=-14\left(1\right)\\4x+y=-7\left(2\right)\end{matrix}\right.\)
Lấy \(\left(2\right)-\left(1\right)\),ta được: \(7y=7\Rightarrow y=1\Rightarrow2x=-7+3=-4\Rightarrow x=-2\)
2) \(P=\left(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}\right).\dfrac{\sqrt{x}}{2x-\sqrt{x}-3}\)
\(=\left(\dfrac{\left(\sqrt{x}\right)^3-1}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}\right)^3+1}{\sqrt{x}\left(\sqrt{x}+1\right)}+\dfrac{x+1}{\sqrt{x}}\right).\dfrac{\sqrt{x}}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\left(\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}-\dfrac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}+\dfrac{x+1}{\sqrt{x}}\right).\dfrac{\sqrt{x}}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\left(\dfrac{x+\sqrt{x}+1}{\sqrt{x}}-\dfrac{x-\sqrt{x}+1}{\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}\right).\dfrac{\sqrt{x}}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{x+2\sqrt{x}+1}{\sqrt{x}}.\dfrac{\sqrt{x}}{\left(2x-3\right)\left(x+1\right)}=\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}}.\dfrac{\sqrt{x}}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}+1}{2\sqrt{x}-3}\)
