Let a,b and c be the three sides of a triangle. Show that $\dfrac 1a+\dfrac 1b+\dfrac 1c\le \dfrac 1{a+b-c}+\dfrac 1{a-b+c}+\dfrac 1{-a+b+c}.$
How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$?