$$4 { x }^{ 2 } + \frac{ 1 }{ 4 { x }^{ 2 } } -2+4x- \frac{ 1 }{ x }$$
$4x^{2}+4x-2-\frac{1}{x}+\frac{1}{4x^{2}}$
$$\frac{\left(4x^{2}-2+4x\right)\times 4x^{2}}{4x^{2}}+\frac{1}{4x^{2}}-\frac{1}{x}$$
$$\frac{\left(4x^{2}-2+4x\right)\times 4x^{2}+1}{4x^{2}}-\frac{1}{x}$$
$$\frac{16x^{4}-8x^{2}+16x^{3}+1}{4x^{2}}-\frac{1}{x}$$
$$\frac{16x^{4}-8x^{2}+16x^{3}+1}{4x^{2}}-\frac{4x}{4x^{2}}$$
$$\frac{16x^{4}-8x^{2}+16x^{3}+1-4x}{4x^{2}}$$
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$\frac{\left(2x-1\right)\left(2x+1\right)\left(x-\frac{-\sqrt{2}-1}{2}\right)\left(x-\frac{\sqrt{2}-1}{2}\right)}{x^{2}}$
