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If ((sqrt2x))/((sqrt3x - 1)) = 3/2, solve for x. Express your answer as a simplified fraction.

 Feb 20, 2018
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Solve for x:

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

 

Cross multiply:

2 sqrt(2) sqrt(x) = 3 (sqrt(3) sqrt(x) - 1)

 

Subtract 3 sqrt(3) sqrt(x) from both sides and collect in terms of sqrt(x):

(2 sqrt(2) - 3 sqrt(3)) sqrt(x) = -3

 

Divide both sides by 2 sqrt(2) - 3 sqrt(3):

sqrt(x) = -3/(2 sqrt(2) - 3 sqrt(3))

 

Raise both sides to the power of two:

x = 9/(2 sqrt(2) - 3 sqrt(3))^2 = 315/361 + (108 sqrt(6))/361

 Feb 20, 2018

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