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If X = `(6ab)/(A + B)` Find the Value of `(X + 3a)/(X - 3a) = (X + 3b)/(X - 3b)` - Mathematics

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Question

if x = `(6ab)/(a + b)` find the value of `(x + 3a)/(x - 3a) = (x + 3b)/(x - 3b)`

Solution

`x = (6ab)/(a + b)`

`=> x/(3a) = (2b)/(a + b)`

Aplying compinendo and dividendo

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

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

Again x = `(6ab)/(a + b)`

`=> x/(3b) = (2a)/(a + b)`

Applying componendo and dividendo

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

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

From (1) and (2)

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

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

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

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 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Exercise 7(C) | Q: 6.1 | Page no. 101

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Solution If X = `(6ab)/(A + B)` Find the Value of `(X + 3a)/(X - 3a) = (X + 3b)/(X - 3b)` Concept: Componendo and Dividendo Properties.
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