6. There are the following three propositions:
(甲) If $\alpha, \beta$ are unequal irrational numbers, then $\alpha \beta + \alpha - \beta$ is an irrational number;
(乙) If $\alpha, \beta$ are unequal irrational numbers, then $\frac{\alpha - \beta}{\alpha + \beta}$ is an irrational number;
(丙) If $\alpha, \beta$ are unequal irrational numbers, then $\sqrt{\alpha} + \sqrt[3]{\beta}$ is an irrational number.

The number of correct propositions is ( ).
(A) 0
(B) 1
(C) 2
(D) 3
6. (A)
$$
\because \alpha \beta+\alpha-\beta=\alpha \beta+\alpha-\beta-1+1=(\alpha-1)(\beta+
$$
1) +1 , if we let $\alpha=1+\sqrt{2}, \beta=-1+\sqrt{2}$, then $\alpha \beta+\alpha-\beta$ is a rational number. $\therefore$ (A) is incorrect;
If we let $\alpha=2 \sqrt{2}, \beta=\sqrt{2}$, then $\frac{\alpha-\beta}{\alpha+\beta}$ is a rational number. $\therefore$ (B) is incorrect;
If we let $\alpha=\sqrt[3]{2}, \beta=-\sqrt{2}$, then $\sqrt{\alpha}+\sqrt[3]{\beta}=0$ is a rational number. $\therefore$ (C) is incorrect.