If H is the harmonic mean between a and b,the | vedclass

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(A) The harmonic mean $H$ between $a$ and $b$ is given by $H = \frac{2ab}{a+b}$.Substituting this into the expression $\frac{1}{H - a} + \frac{1}{H -

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$\frac{1}{a} + \frac{1}{b}$

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(A) The harmonic mean $H$ between $a$ and $b$ is given by $H = \frac{2ab}{a+b}$.Substituting this into the expression $\frac{1}{H - a} + \frac{1}{H - b}$:$\frac{1}{\frac{2ab}{a+b} - a} + \frac{1}{\frac{2ab}{a+b} - b} = \frac{a+b}{2ab - a(a+b)} + \frac{a+b}{2ab - b(a+b)}$$= \frac{a+b}{2ab - a^2 - ab} + \frac{a+b}{2ab - ab - b^2} = \frac{a+b}{ab - a^2} + \frac{a+b}{ab - b^2}$$= \frac{a+b}{a(b-a)} + \frac{a+b}{b(a-b)} = \frac{a+b}{a(b-a)} - \frac{a+b}{b(b-a)}$$= \frac{b(a+b) - a(a+b)}{ab(b-a)} = \frac{(a+b)(b-a)}{ab(b-a)} = \frac{a+b}{ab} = \frac{1}{b} + \frac{1}{a}$.

If $H$ is the harmonic mean between $a$ and $b$,then what is the value of $\frac{1}{H - a} + \frac{1}{H - b}$?

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