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 ? ?->(Show Answer!)

1. 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 ?

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By: anil on 05 May 2019 02.57 pm

$$frac{b-c}{a}+frac{a+c}{b}+frac{a-b}{c}=1$$ => $$frac{b-c}{a}+frac{a-b}{c}+frac{a+c}{b} - 1 = 0$$ => $$frac{b-c}{a}+frac{a-b}{c}+frac{a+c-b}{c} = 0$$ => $$frac{c-b}{a}+frac{b-a}{c} = frac{a+c-b}{b}$$ => $$frac{c^{2}-bc+ab-a^{2}}{ac} = frac{a+c-b}{b}$$ => $$frac{(c^{2}-a^{2}) - (bc-ab)}{ac} = frac{a+c-b}{b}$$
=> $$frac{(c-a)(c+a) -b(c-a)}{ac} = frac{a+c-b}{b}$$
=> $$frac{(c-a)(c+a-b)}{ac} = frac{a+c-b}{b}$$
=> $$frac{c-a}{ac} = frac{1}{b}$$
=> $$frac{c}{ac} - frac{a}{ac} = frac{1}{b}$$
=> $$frac{1}{a} - frac{1}{c} = frac{1}{b}$$

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