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# If X = (2ab)/(A + B) Find the Value Of (X + A)/(X - A) + (X +B)/(X - B) - Mathematics

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#### Question

if x = (2ab)/(a + b) find the value of  (x + a)/(x - a) + (x +b)/(x - b)

#### Solution

x = (2ab)/(a + b)

x/a = (2b)/(a + b)

Applying componendo and dividendo

(x + a)/(x - a) = (2b + a + b)/(2b - a - b)

(x = a)/(x - a) = (3b + a)/(b - a)  ...(1)

Also x = (2ab)/(a + b)

x/b = (2a)/(a + b)

Apllying componendo and dividendo

(x + b)/(x - b) = (2a + a + b)/(2a - a - b)

(x + a)/(x - a) = (3b + a)/(b - a)  ...(1)

Also x = (2ab)/(a + b)

x/b = (2a)/(a + b)

Applying componendo and dividendo

(x + b)/(x - b) = (2a + a + b)/(2a - a - b)

(x + b)/(x - b) = (3a + b)/(a - b)   ....(2)

From (1) and (2)

(x + a)/(x - a) = (2a + a + b)/(2a - a - b)

(x + b)/(x - b) = (3a + b)/(a - b) ....(2)

From (1) and (2)

(x + a)/(x - a) + (x + a)/(x - b) = (3b  + a)/(b - a) + (3a + b)/(a - b)

(x + a)/(x - a) + (x + b)/(x - b)= (-3b - a + 3a + b)/(a- b)

(x + a)/(x - a) + (x + b)/(x - b) = (2a - 2b)/(a - b)

(x + a)/(x - a) + (x + b)/(x - b) = (2a - 2b)/(a - b) = 2

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If X = (2ab)/(A + B) Find the Value Of (X + A)/(X - A) + (X +B)/(X - B) Concept: Componendo and Dividendo Properties.