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How to solve the following quadratic inequality:

0.3 < 2x/(x^2 + 4) < 0.5

The call to solve function return the following output:

sage: 
sage: solve( [(2*x / (4+x**2)) < .5 , (2*x / (x**2 + 4)) > .3 ], x, to_poly_serve=True )
[[-2*x/(x^2 + 4) + 0.5 > 0, 2*x/(x^2 + 4) - 0.3 > 0]]
sage:

By hand calculation I found the following answer (2/3, 2) U (2, 6).

How to solve the following quadratic inequality:

0.3 $$0.3 < 2x/(x^2 \frac{2x}{x^{2} + 4) < 0.54} <0.5$$

The call to solve function return the following output:

sage: 
sage: solve( [(2*x / (4+x**2)) < .5 , (2*x / (x**2 + 4)) > .3 ], x, to_poly_serve=True )
[[-2*x/(x^2 + 4) + 0.5 > 0, 2*x/(x^2 + 4) - 0.3 > 0]]
sage:

By hand calculation I found the following answer (2/3, 2) U (2, 6).

How to solve the following quadratic inequality:

$$0.3 < \frac{2x}{x^{2} + 4} <0.5$$

The call to solve function return the following output:

sage: 
sage: solve( [(2*x / (4+x**2)) < .5 , (2*x / (x**2 + 4)) > .3 ], x, to_poly_serve=True )
[[-2*x/(x^2 + 4) + 0.5 > 0, 2*x/(x^2 + 4) - 0.3 > 0]]
sage:

By hand calculation I found the following answer (2/3, $(2/3, 2) U \cup (2, 6).6)$.