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 ?
A. $$\frac{1}{c} = \frac{1}{a} + \frac{1}{b}$$
B. $$\frac{1}{a} = \frac{1}{b} + \frac{1}{c}$$
C. $$\frac{1}{b} = \frac{1}{a} - \frac{1}{c}$$
D. $$\frac{1}{b} = \frac{1}{a} + \frac{1}{c}$$
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & \frac{{b - c}}{a}{\text{ + }}\frac{{a + c}}{b}{\text{ + }}\frac{{a - b}}{c} = 1 \cr & a - b + c \ne 0 \cr & {\text{Let }}b = c \cr & \therefore \frac{{b - b}}{a}{\text{ + }}\frac{{a + b}}{b}{\text{ + }}\frac{{a - b}}{b} = 1 \cr & \Rightarrow 0 + \frac{a}{b} + 1 + \frac{a}{b} - 1 = 1 \cr & \Rightarrow \frac{a}{b} + \frac{a}{b} = 1 \cr & \Rightarrow \frac{1}{b} + \frac{1}{b} = \frac{1}{a} \cr & {\text{We take }}b = c \cr & \therefore \boxed{\frac{1}{b} + \frac{1}{c} = \frac{1}{a}} \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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