Question

If h is harmonic mean between a and b then H+a/H-a + H+a/H-b =

Answer 1

Answer:

$a/b + 3$

Step-by-step explanation:

Given H is the harmonic mean of a and b

i.e, $H = \frac{2}{\frac{1}{a} + \frac{1}{b} }$  

The harmonic mean is the reciprocal of the average of the reciprocals

i.e, The formula is:

Harmonic Mean  = $\frac{n}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + ... }$

Where a,b,c,... are the values, and n is how many values.

Therefore, $H = \frac{2ab}{a+b}$

Consider, $\frac{H+a}{H-a} + \frac{H+a}{H-b}$

⇒ $\frac{\frac{2ab}{a+b} + a }{\frac{2ab}{a+b} - a} + \frac{\frac{2ab}{a+b} + a}{\frac{2ab}{a+b} - b }$

⇒ $(a^{2} + 3ab)/(ab - a^{2}) + (a^{2} + 3ab)/(ab - b^{2})$

⇒ $((a^{2} + 3ab)(ab - b^{2})+(a^2 + 3ab)(ab - a^2))/((ab - a^2)(ab - b^2))$

⇒ $(a^2 + 3ab)[(ab - a^2)+(ab - b^2)]/(ab - a^2)(ab - b^2)$

⇒ $(a^2 + 3ab)[-(a-b)^2]/(-ab(a-b)^2)$

⇒ $(a^2 + 3ab)/ab$

⇒ $a/b + 3$

Answer 2

Answer:

Step-by-step explanation:

=a/b+3=a