$$3x^{2}-4x-7\div x^{2}-1-x$$
$3x^{2}-5x-1-\frac{7}{x^{2}}$
$$3x^{2}-5x-\frac{7}{x^{2}}-1$$
$$\frac{\left(3x^{2}-5x-1\right)x^{2}}{x^{2}}-\frac{7}{x^{2}}$$
$$\frac{\left(3x^{2}-5x-1\right)x^{2}-7}{x^{2}}$$
$$\frac{3x^{4}-5x^{3}-x^{2}-7}{x^{2}}$$
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$\frac{\left(x+1\right)\left(3x^{3}-8x^{2}+7x-7\right)}{x^{2}}$