\[\frac{2}{\sqrt{3}-2}\]
1
Rationalize the denominator: 23−2⋅3+23+2=23+432−22\frac{2}{\sqrt{3}-2} \cdot \frac{\sqrt{3}+2}{\sqrt{3}+2}=\frac{2\sqrt{3}+4}{{\sqrt{3}}^{2}-{2}^{2}}.
23+432−22\frac{2\sqrt{3}+4}{{\sqrt{3}}^{2}-{2}^{2}}

2
Factor out the common term 22.
2(3+2)32−22\frac{2(\sqrt{3}+2)}{{\sqrt{3}}^{2}-{2}^{2}}

3
Use this rule: x2=x{\sqrt{x}}^{2}=x.
2(3+2)3−22\frac{2(\sqrt{3}+2)}{3-{2}^{2}}

4
Simplify  22{2}^{2}  to  44.
2(3+2)3−4\frac{2(\sqrt{3}+2)}{3-4}

5
Simplify  3−43-4  to  −1-1.
2(3+2)−1\frac{2(\sqrt{3}+2)}{-1}

6
Move the negative sign to the left.
−2(3+2)-2(\sqrt{3}+2)

Done

Decimal Form: -7.464102
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