Rationalize the denominator and simplify. $$ \frac{9}{3 \sqrt{3}-2} $$

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UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \frac{9}{3 \sqrt{3}-2} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{9}{3\sqrt{3}-2}$$
- step1: Multiply by the Conjugate:
  $$\frac{9\left(3\sqrt{3}+2\right)}{\left(3\sqrt{3}-2\right)\left(3\sqrt{3}+2\right)}$$
- step2: Multiply the numbers:
  $$\frac{9\left(3\sqrt{3}+2\right)}{23}$$
- step3: Multiply the numbers:
  $$\frac{27\sqrt{3}+18}{23}$$
The rationalized form of $$ \frac{9}{3 \sqrt{3}-2} $$ is $$ \frac{27\sqrt{3}+18}{23} $$.
The simplified form is $$ \frac{27\sqrt{3}+18}{23} $$.

Rationalize the denominator and simplify.

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