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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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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(D) | Q: 12 | Page no. 102
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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.
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