# Using Properties of Proportion Solve for X: Sqrt(X + 1) + Sqrt(X - 1))/(Sqrt(X + 1) - Sqrt(X - 1)) = (4x - 1)/2 - Mathematics

Using properties of proportion solve for x:

(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2

#### Solution

(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2

Applying componendo and dividendo

(sqrt(x + 1) + sqrt(x - 1) + sqrt(x + 1) - sqrt(x - 1))/(sqrt(x + 1) + sqrt(x - 1) - sqrt(x + 1) + sqrt(x - 1)) = (4x - 1 + 2)/(4x - 1 - 2)

(2sqrt(x + 1))/(2sqrt(x - 1)) = (4x + 1)/(4x - 3 )

Squaring both sides

(x + 1)/(x - 1) = (16x^2 + 1 + 8x )/(16x^2 + 9 - 24x)

Applying componedo and dividendo

(x + 1 + x - 1)/(x + 1 - x + 1) = (16x^2 + 1 + 8x + 16x^2 + 9 - 24x)/(16x^2 + 1 + 8x - 16x^2 - 9 + 24x)

(2x)/2 = (32x^2 + 10 - 16x )/(32x - 8)

x = (16x^2 + 5 - 8x)/(16x - 4)

16x^2 - 4x = 16x^2 + 5 - 8x

4x = 5

x = 5/4

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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 11.2 | Page 102