`A` `=` `(\sqrt{2/3} + \sqrt{50/3} - \sqrt{24})` `×` $\sqrt{6}$
`=` `( \sqrt{2/3} + 5\sqrt{2/3} - 2\sqrt{6})` `×` $\sqrt{6}$
`=` `(2\sqrt{6}- 2\sqrt{6})` `×` $\sqrt{6}$
`=` `0` `×` $\sqrt{6}$
`=` `0`
`B` `=` `[(\sqrt{14}-\sqrt{7})/(\sqrt{2}-1)]` `+` `[(\sqrt{15}-\sqrt{5})/(\sqrt{3}-1)]` `÷` `1/(\sqrt{7}-\sqrt{5})`
`=` `[{\sqrt{7}(\sqrt{2}-1)}/(\sqrt{2}-1)]` `+` `[{\sqrt{5}(\sqrt{3}-1)}/(\sqrt{3}-1)]` `×` `(\sqrt{7}-\sqrt{5})/1`
`=` `(\sqrt{7}+\sqrt{5})` `×` `(\sqrt{7}-\sqrt{5})`
`=` `7` `-` `5` `=` `2`
`2,`
$\sqrt{3x}$ `-` $5\sqrt{12x}$ `+` $7\sqrt{27x}$ `=` `12`
⇔ $\sqrt{3x}$ `-` $10\sqrt{3x}$ `+` $21\sqrt{3x}$ `=` `12`
⇔ $\sqrt{3x}$ `×` `(1-10+21)` `=` `12`
⇔ $\sqrt{3x}$ `×` `12` `=` `12`
⇔ $\sqrt{3x}$ `=` `1`
⇔ $\sqrt{3x}$ `=` $\sqrt{1}$
⇔ `3x` `=` `1`
⇔ `x` `=` `1/3`
