SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Fractional Equations

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Question 172673This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Fractional Equations
(1/x^2)-x^2 over (1/x)+x=3/2
I was also wondering if you would include the domain restriction and the LCD PLEASE! This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
[(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.