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If X = `(2ab)/(A + B)` Find the Value Of `(X + A)/(X - A) + (X +B)/(X - B)` - ICSE Class 10 - 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`

  Is there an error in this question or solution?

APPEARS IN

 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7D | Q: 14

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Solution 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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