$H_1,H_2$ are $2H.M^{\prime }.s$ between $a$ and $b$ then $\frac{H_1+H_2}{H_1,H_2}=$

The correct option is C $\frac{a+b}{ab}$

since $H_1,H_2$ are two H.M & between a and b

so,

$a,H_1,H_2,b$ is a H.P

$\Rightarrow \frac{1}{a},\frac{1}{H_1},\frac{1}{H_2},\frac{1}{b}$ is an A.P

$\Rightarrow \frac{1}{H_1}-\frac{1}{a}=\frac{1}{b}-\frac{1}{H_2}$

$\Rightarrow \frac{1}{H_1}+\frac{1}{H_2}=\frac{1}{b}+\frac{1}{a}$

$\Rightarrow \frac{H_1+H_2}{H_1{H}_2}=\frac{a+b}{ab}$