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

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

`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`

Concept: Componendo and Dividendo Properties

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Chapter 7 Ratio and Proportion (Including Properties and Uses)
Exercise 7 (C) | Q 6.1 | Page 101