If $$\frac{{b - c}}{a}$$  + $$\frac{{a + c}}{b}$$  + $$\frac{{a - b}}{c}$$  = 1 and a - b + c ≠ 0 then which one of the following relations is true ?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{b - c}}{a}{\text{ + }}\frac{{a + c}}{b}{\text{ + }}\frac{{a - b}}{c} = 1 \cr & a - b + c \ne 0 \cr & {\text{Let }}b = c \cr & \therefore \frac{{b - b}}{a}{\text{ + }}\frac{{a + b}}{b}{\text{ + }}\frac{{a - b}}{b} = 1 \cr & \Rightarrow 0 + \frac{a}{b} + 1 + \frac{a}{b} - 1 = 1 \cr & \Rightarrow \frac{a}{b} + \frac{a}{b} = 1 \cr & \Rightarrow \frac{1}{b} + \frac{1}{b} = \frac{1}{a} \cr & {\text{We take }}b = c \cr & \therefore \boxed{\frac{1}{b} + \frac{1}{c} = \frac{1}{a}} \cr} $$