If a, b, c are in H.P. then the value of is

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If a, b, c are in H.P. then the value of
$\frac{b + a}{b - a} + \frac{b + c}{b - c}$ is

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a, b, c in H.P

\Rightarrow \frac{1}{a},\frac{1}{b},\frac{1}{c}

in A.P
Let

\frac{1}{a} - a, - d

\frac{1}{b} = a,

\frac{1}{c} = a, + d

.
Now,

\frac{b + a}{b - a} + \frac{b + c}{b - c} = \frac{\frac{1}{a_{1}} + \frac{1}{a_{1} - d}}{\frac{1}{a_{1}} - \frac{1}{a_{1} - d}} + \frac{\frac{1}{a_{1}} + \frac{1}{a_{1} + d}}{\frac{1}{a_{1}} - \frac{1}{a_{1} + d}}

= \frac{2a_{1} - d}{- d} + \frac{2a_{1} + d}{d}

= \frac{2d}{d} = 2

Source: Grass-G / M-06 Mathematics Paper 14 October.docx

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