Bonjour,
6)
[tex]L=\frac{x^{2} }{x\sqrt{x} } \\\\=\frac{x}{\sqrt{x} } \\\\=\frac{x\sqrt{x} }{\sqrt{x} \sqrt{x} } \\\\=\frac{x\sqrt{x} }{x} \\\\=\sqrt{x}[/tex]
7)
[tex]M=\sqrt{x} -\frac{1}{\sqrt{x} } \\\\=\frac{\sqrt{x} *\sqrt{x} }{\sqrt{x} } -\frac{1}{\sqrt{x} } \\\\=\frac{x-1}{\sqrt{x} }[/tex]
[tex]N=2-\sqrt{x} +\frac{1}{\sqrt{x}+1 } \\\\=\frac{2(\sqrt{x}+1) }{\sqrt{x}+1 } -\frac{\sqrt{x}(\sqrt{x}+1) }{\sqrt{x}+1 } +\frac{1}{\sqrt{x} +1} \\\\=\frac{2\sqrt{x}+2 }{\sqrt{x}+1 } -\frac{x+\sqrt{x} }{\sqrt{x}+1 } +\frac{1}{\sqrt{x}+1 } \\\\=\frac{2\sqrt{x}+2-x-\sqrt{x}+1 }{\sqrt{x} +1} \\\\=\frac{\sqrt{x} -x+3}{\sqrt{x}+1 }[/tex]
