Divide. Write the answer in simplified form. $$ \frac{4 x^{2}-1}{x^{2}-3 x} \div \frac{2 x^{2}+5 x+2}{x^{2}-x-6}=\square $$

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Calculate or simplify the expression $$ (4x^{2}-1)/(x^{2}-3x) \div (2x^{2}+5x+2)/(x^{2}-x-6) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\left(4x^{2}-1\right)}{\left(x^{2}-3x\right)}\div \left(2x^{2}+5x+2\right)}{\left(x^{2}-x-6\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{4x^{2}-1}{x^{2}-3x}\div \left(2x^{2}+5x+2\right)}{x^{2}-x-6}$$
- step2: Divide the terms:
  $$\frac{\frac{2x-1}{\left(x^{2}-3x\right)\left(x+2\right)}}{x^{2}-x-6}$$
- step3: Multiply by the reciprocal:
  $$\frac{2x-1}{\left(x^{2}-3x\right)\left(x+2\right)}\times \frac{1}{x^{2}-x-6}$$
- step4: Multiply the terms:
  $$\frac{2x-1}{\left(x^{2}-3x\right)\left(x+2\right)\left(x^{2}-x-6\right)}$$
- step5: Simplify:
  $$\frac{2x-1}{\left(x-3\right)^{2}\left(x+2\right)^{2}x}$$
- step6: Expand the expression:
  $$\frac{2x-1}{x^{5}-2x^{4}-11x^{3}+12x^{2}+36x}$$
The result of the division is $$ \frac{2x-1}{x^{5}-2x^{4}-11x^{3}+12x^{2}+36x} $$.
$$ \frac{2x-1}{x^{5}-2x^{4}-11x^{3}+12x^{2}+36x} $$

Divide. Write the answer in simplified form.

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