The solution to the equation is x = 3
Given the equation
1/x = x+3/2x^2
Cross multiply
2x^2 = x(x+3)
2x^2 = x^2 + 3x
Equate the expression to zero
2x^2-x^2-3x = 0
x^2 - 3x = 0
Add 3x to both sides
x^2 - 3x + 3x = 3x
x^2 = 3x
x = 3
Hence the solution to the equation is x = 3
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