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(B) The harmonic mean $H$ between $a$ and $b$ is given by $H = \frac{2ab}{a + b}$.We need to evaluate the expression $\frac{H + a}{H - a} + \frac{H +

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$2$

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(B) The harmonic mean $H$ between $a$ and $b$ is given by $H = \frac{2ab}{a + b}$.We need to evaluate the expression $\frac{H + a}{H - a} + \frac{H + b}{H - b}$.First,simplify the expression:$\frac{H + a}{H - a} + \frac{H + b}{H - b} = \frac{(H + a)(H - b) + (H + b)(H - a)}{(H - a)(H - b)}$$= \frac{(H^2 - Hb + aH - ab) + (H^2 - Ha + bH - ab)}{H^2 - Hb - aH + ab}$$= \frac{2H^2 - 2ab}{H^2 - H(a + b) + ab}$.Since $H = \frac{2ab}{a + b}$,we have $H(a + b) = 2ab$.Substituting this into the denominator:Denominator $= H^2 - 2ab + ab = H^2 - ab$.Thus,the expression becomes $\frac{2(H^2 - ab)}{H^2 - ab} = 2$.

If the harmonic mean between $a$ and $b$ is $H$,then $\frac{H + a}{H - a} + \frac{H + b}{H - b} = $

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