1. Simplify the expression

$$
\left(x+\sqrt[3]{3 \cdot \sqrt{\frac{x^{3}-1}{9}+\frac{x-x^{2}}{3}}}\right) \cdot(x-\sqrt{x-1})
$$
1. Simplify the expression: $\left(x+\sqrt[3]{3 \cdot \sqrt{\frac{x^{3}-1}{9}+\frac{x-x^{2}}{3}}}\right) \cdot(x-\sqrt{x-1})=\left(x+\sqrt[3]{3 \cdot \sqrt{\frac{x^{3}-1+3 x-3 x^{2}}{9}}}\right)$. $(x-\sqrt{x-1})=\left(x+\sqrt[6]{(x-1)^{3}}\right) \cdot(x-\sqrt{x-1})=(x+\sqrt{x-1}) \cdot(x-\sqrt{x-1})=x^{2}-x+1$.

Expanding to a common denominator $\sqrt[3]{3 \cdot \sqrt{\frac{x^{3}-1+3 x-3 x^{2}}{9}}}$

Conclusion $\sqrt[6]{3^{2} \cdot \frac{x^{3}-1+3 x-3 x^{2}}{9}}$. .1 point

Writing $\sqrt[6]{(x-1)^{3}}$ .1 point

Conclusion $\sqrt[6]{(x-1)^{3}}=\sqrt{x-1}$

1 point

Multiplying the brackets

1 point

Result $x^{2}-x+1$

1 point