Simplifying a fraction by only multiplying one side by the denominator? Given the problem: $x\sqrt{3} = 6$
We can solve it this way:
$ x = \frac{ 6 } {\sqrt{3} } \times \frac{ \sqrt{3} } { \sqrt{3} } $
$ x = \frac{ 6 \sqrt{3} } {3} $
$ x = 2 \sqrt{3} $
In the first step, why can we multiply only the right side by $\sqrt{3}$? Shouldn't both sides be modified in the same way to keep them balanced?

To get from here:
$x\sqrt{3} = 6$
to here:
$ x = \frac{ 6 } {\sqrt{3} } \times \frac{ \sqrt{3} } { \sqrt{3} }, $
both sides of the equation were divided by $\sqrt{3},$ not multiplied by $\sqrt{3}.$
