If H is the harmonic mean between $a$ and $b$,then show that $\frac{1}{H-a}+\frac{1}{H-b} = \frac{1}{a} + \frac{1}{b}$ and $\frac{H+a}{H-a}+\frac{H+b}{H-b} = 2$
I substituted $\displaystyle H = \frac{2ab}{a+b}$, then tried some algebraic manipulation, but I am not getting there.
Are they even valid? If yes, could somebody give me some ideas how to approach these?