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

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(A) Given that $H$ is the harmonic mean between $a$ and $b$,we have $H = \frac{2ab}{a + b}$.Substituting this into the expression $\frac{1}{H - a} + \

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

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(A) Given that $H$ is the harmonic mean between $a$ and $b$,we have $H = \frac{2ab}{a + b}$.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)}$$= \frac{a + b}{b - a} \left( \frac{1}{a} - \frac{1}{b} \right) = \frac{a + b}{b - a} \left( \frac{b - a}{ab} \right)$$= \frac{a + b}{ab} = \frac{1}{b} + \frac{1}{a}$.

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

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