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Addition and Subtraction of a Matrix

If 1/(b-a) + ...

Question

If 1/(b-a) + 1/(b-c) = 1/a + 1/c then a, b, c are in

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

a, b, c

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

, then a, b, c are in

\frac{b + c - a}{a}, \frac{c + a - b}{b}, \frac{a + b - c}{c}

are in A.P.,then

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

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

A . P

\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}

G . P

\frac{b + c - a}{a}, \frac{c + a - b}{b}, \frac{a + b - c}{c}

are in A.P., then

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

are also in A.P.

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