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

Divide. Write the answer in simplified form

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