Question 172673
[(1/x^2)-x^2 / [(1/x)+x] = 3/2
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Since x is in the denominator, x cannot be zero.
lcd of the numerator is x^2 ; lcd of the denominator is "x".
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Simplify:

[(1-x^4)/x^2] / [(1+x^2)/x] = 3/2

Invert the denominator and multiply:

[(1-x^4)/x^2] * [x/(1+x^2)] = 3/2

Cancel where you can to get:

[(1-x^2)/x] = 3/2
Cross multiply to get:
2(1-x^2) = 3x
2 - 2x^2 = 3x
2x^2 + 3x -1 = 0
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Use the Quadratic Formula to get:

x = [-3 +- sqrt(9 -4*2*-1)]/4

x = [-3 +- sqrt(17)]/4

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Cheers,
stan H.