If x,y,z `gt` 0 and x + y + z = 1, the prove that
`(2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3`.

Explanation

Using `A.M. ge H.M.` we have
`((x+y)+(y+z)+(z+x))/(3) ge (3)/((1)/(x+y)+(1)/(y+z)(1)/(z+x))`
` rArr 2(x+y+z)((1)/(x+y)+(1)/(y+z)+(1)/(z+x))ge 9`
`rArr 2((x+y+z)/(x+y)+(x+y+z)/(y+z)+(x+y+z)/(z+x))ge 9`
`rArr 2[(1+(z)/(x+y))+(1+(x)/(y+z))+(1+(y)/(x+z))]ge 9`
` rArr 2((x)/(y+z)+(y)/(z+x)+(z)/(x+y))ge3`
`rArr 2((x)/(1-x)+(y)/(1-y)+(z)/(1-z)) ge3`