Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{ 5+2 \sqrt{ 3 } }{ 7+4 \sqrt{ 3 } } =a-6 \sqrt{ 3 }$$

Answer

a=(5+2*sqrt(3))/(7+4*sqrt(3))+6*sqrt(3)

Solution


Add \(6\sqrt{3}\) to both sides.
\[\frac{5+2\sqrt{3}}{7+4\sqrt{3}}+6\sqrt{3}=a\]
Switch sides.
\[a=\frac{5+2\sqrt{3}}{7+4\sqrt{3}}+6\sqrt{3}\]
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