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 ?

$$\frac{b-c}{a}+\frac{a+c}{b}+\frac{a-b}{c}=1$$

=> $$\frac{b-c}{a}+\frac{a-b}{c}+\frac{a+c}{b} - 1 = 0$$

=> $$\frac{b-c}{a}+\frac{a-b}{c}+\frac{a+c-b}{c} = 0$$

=> $$\frac{c-b}{a}+\frac{b-a}{c} = \frac{a+c-b}{b}$$

=> $$\frac{c^{2}-bc+ab-a^{2}}{ac} = \frac{a+c-b}{b}$$

=> $$\frac{(c^{2}-a^{2}) - (bc-ab)}{ac} = \frac{a+c-b}{b}$$

=> $$\frac{(c-a)(c+a) -b(c-a)}{ac} = \frac{a+c-b}{b}$$

=> $$\frac{(c-a)(c+a-b)}{ac} = \frac{a+c-b}{b}$$

=> $$\frac{c-a}{ac} = \frac{1}{b}$$

=> $$\frac{c}{ac} - \frac{a}{ac} = \frac{1}{b}$$

=> $$\frac{1}{a} - \frac{1}{c} = \frac{1}{b}$$