Question

Докажите тождество:​

Answer 1

$\dfrac{3x-1}{\sqrt{3x}-1}-\sqrt{3x}=\dfrac{3x-1-\sqrt{3x}(\sqrt{3x}-1)}{\sqrt{3x}-1}=\dfrac{3x-1-3x+\sqrt{3x}}{\sqrt{3x}-1}=\\ \\ \\ =\dfrac{\sqrt{3x}-1}{\sqrt{3x}-1}=1,~~~~ x\ne \dfrac{1}{3}$