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(C) Given that $H$ is the harmonic mean between $a$ and $b$,we have $H = \frac{2ab}{a + b}$.We need to evaluate the expression $\frac{1}{H - a} + \fra

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Given that $H$ is the harmonic mean between $a$ and $b$,we have $H = \frac{2ab}{a + b}$.We need to evaluate the expression $\frac{1}{H - a} + \frac{1}{H - b}$.Substituting the value of $H$:$\frac{1}{\frac{2ab}{a + b} - a} + \frac{1}{\frac{2ab}{a + b} - b} = \frac{1}{\frac{2ab - a(a + b)}{a + b}} + \frac{1}{\frac{2ab - b(a + 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(a - b)} + \frac{a + b}{b(a - b)} = \frac{a + b}{a - b} \left( \frac{1}{b} - \frac{1}{a} \right)$$= \frac{a + b}{a - b} \left( \frac{a - b}{ab} \right) = \frac{a + b}{ab} = \frac{a}{ab} + \frac{b}{ab} = \frac{1}{b} + \frac{1}{a}$.Thus,the value is $\frac{1}{a} + \frac{1}{b}$.

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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