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Q.
If $a, b, c$ are in H.P. then the value of $\frac{b+a}{b-a}+\frac{b+c}{b-c}$ is :
Sequences and Series
Solution:
Put $b=\frac{2 a c}{a+c} $
$\Rightarrow \frac{b+a}{b-a}+\frac{b+c}{b-c}=\frac{\frac{2 a c}{a+c}+a}{\frac{2 a c}{a+c}-a}+\frac{\frac{2 a c}{a+c}+c}{\frac{2 a c}{a+c}-c}$
$=\frac{a+3 c}{c-a}+\frac{3 a+c}{a-c}=\frac{a+3 c-3 a-c}{c-a}=\frac{2(c-a)}{c-a}=2$