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# Using Properties of Proportion Solve for X: (3x + Sqrt(9x^2 - 5))/(3x - Sqrt(9x^2 - 5)) = 5 - Mathematics

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#### Question

Using properties of proportion solve for x:

(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5

#### Solution

(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5

Applying componendo and dividendo

(3x + sqrt(9x^2 - 5) + 3x - sqrt(9x^2 - 5))/(3x sqrt(9x^2 - 5) - 3x + sqrt(9x^2 - 5)) = (5 + 1)/(5 - 1)

(6x)/(2sqrt(9x^2 - 5)) = 6/4

x/sqrt(9x^2 - 5) = 1/2

Squaring both sides

x^2/(9x^2 - 5) = 1/4

4x^2 - 9x^2 - 5

5x^2 = 5

5x^2  = 5

x^2 = 1

x = 1

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