Question

$\frac{x+2 \sqrt{6} }{ \sqrt{3} } - \sqrt{12} = \sqrt{18}$

Valor de X, por favor.

Answer 1

$\frac{x+2 \sqrt{6} }{ \sqrt{3} } - \sqrt{12} = \sqrt{18} \\ \\ \frac{(x+2 \sqrt{6})* \sqrt{3} }{ \sqrt{3}* \sqrt{3} } - \sqrt{4*3}= \sqrt{2*9} \\ \\ \frac{x \sqrt{3} +2 \sqrt{18}) }{ \sqrt{9} } -2 \sqrt{3}= 3\sqrt{2} \\ \\ \frac{x \sqrt{3} +2 \sqrt{2*9}) }{ 3 } -2 \sqrt{3}= 3\sqrt{2} \\ \\ \frac{x \sqrt{3} +6 \sqrt{2}) }{ 3 } -2 \sqrt{3}= 3\sqrt{2} \\ x \sqrt{3}+2 \sqrt{2} -2 \sqrt{3}=3 \sqrt{2} \\ x \sqrt{3}=3 \sqrt{2}-2 \sqrt{2} +2 \sqrt{3} \\ x \sqrt{3}= \sqrt{2}+2 \sqrt{3}$

$x= \frac{ \sqrt{2}+2 \sqrt{3} }{ \sqrt{3} } \\ \\ x=\frac{( \sqrt{2}+2 \sqrt{3}) \sqrt{3} }{ \sqrt{3}* \sqrt{3} } \\ \\ x=\frac{ \sqrt{6}+2 \sqrt{9} }{ \sqrt{9} } \\ \\ x=\frac{ \sqrt{6}+2 *3 }{ 3 } \\ \\ \boxed{\boxed{x= \sqrt{6}+2 }}$