If  $a,b,c$ are in H.P., then 

$\frac{a}{b+c-a},\frac{b}{c+a-b},\frac{c}{a+b-c}$ are in 

 $a,b,c$ are in H.P

$\Rightarrow \frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P

$\Rightarrow \frac{a+b+c}{a}-2,\frac{a+b+c}{b}-2,\frac{a+b+c}{c}-2$  are in A.P

$\Rightarrow \frac{b+c-a}{a},\frac{c+a-b}{b},\frac{a+b-c}{c}$ are in A.P

$\Rightarrow \frac{a}{b+c-a},\frac{b}{c+a-b},\frac{c}{a+b-c}$are in H.P