Rationalize the denominator and simplify. $$ \frac{-3}{4 \sqrt{2}-3} $$

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Calculate or simplify the expression $$ \frac{-3}{4 \sqrt{2}-3} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{-3}{4\sqrt{2}-3}$$
- step1: Multiply by the Conjugate:
  $$\frac{-3\left(4\sqrt{2}+3\right)}{\left(4\sqrt{2}-3\right)\left(4\sqrt{2}+3\right)}$$
- step2: Multiply the numbers:
  $$\frac{-3\left(4\sqrt{2}+3\right)}{23}$$
- step3: Multiply the numbers:
  $$\frac{-12\sqrt{2}-9}{23}$$
- step4: Calculate:
  $$-\frac{12\sqrt{2}+9}{23}$$
The rationalized form of $$ \frac{-3}{4 \sqrt{2}-3} $$ is $$ -\frac{12\sqrt{2}+9}{23} $$.
The simplified form is $$ -\frac{12\sqrt{2}+9}{23} $$.

Rationalize the denominator and simplify.

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