1. If 2x+1/x=2, find the value of x/(2x²+x+1)
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Solving the given equation for x, we find two complex roots to the quadratic equation x^2 - x + 2 = 0:
x = (1 +/- sqrt(7)*i)/2
And
x^2 = (-3 +/- sqrt(7)*i)/2
We can simplify x^2 + x + 2*(1 - x)/x^2 by replacing x with x^2 + 2 to get:
2*(x^2 - 1/x^2)
Substituting the known values for x^2 we get:
(-9 +/- 5*sqrt(7)*i)/4
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