If $a,b,c$ are in harmonic progression, then the value of $\frac{a+b}{a-b}+\frac{c+b}{c-b}$ is:

Solution

1. Since $a,b,c$ are in HP, $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in AP, so $\frac{2}{b}=\frac{1}{a}+\frac{1}{c}$.
2. This implies $b=\frac{2ac}{a+c}$.
3. Substitute $b$ into the expression $\frac{a+b}{a-b}+\frac{c+b}{c-b}$.
4. After algebraic simplification, the expression evaluates to 2.
5. Hence the answer is (B).