lean_workbook_plus_76147

prove that $1. \left( {\frac {x}{\sqrt {y \left( x+y \right) }}}+{\frac {y}{\sqrt {z \left( y+z \right) }}}+{\frac {z}{\sqrt {x \left( z+x \right) }}} \right) \left( \sqrt {{\frac {x}{x+y}}}+\sqrt {{\frac {y}{y+z}}}+\sqrt {{\frac {z}{z+x}}} \right) \geq \frac{9}{2}$