# 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)

#### 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

Concept: Componendo and Dividendo Properties
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#### APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 7 Ratio and Proportion (Including Properties and Uses)
Exercise 7 (C) | Q 6.1 | Page 101