Question

Упростите выражение:

Answer 1

$( \frac{x-1}{x ^{ \frac{1}{3} }-1 }+x ^{ \frac{1}{3} }) \cdot \frac{x^{ \frac{1}{3}-1}}{x^{ \frac{2}{3} }-1 } = \\ \\ =( \frac{x-1+x^{ \frac{2}{3}}- x^{ \frac{1}{3} } }{x ^{ \frac{1}{3} }-1}) \cdot \frac{x^{ \frac{1}{3}-1}}{x^{ \frac{2}{3} }-1 } = \frac{x-x^{ \frac{1}{3} } +x^{ \frac{2}{3}}-1 }{x^{ \frac{2}{3} }-1 } = \frac{x^{ \frac{1}{3} }(x ^{ \frac{2}{3} }-1)+(x ^{ \frac{2}{3} }-1) }{x ^{ \frac{2}{3} }-1}=$

$=\frac{(x ^{ \frac{2}{3} }-1)(x ^{ \frac{1}{3} }+1)}{x ^{ \frac{2}{3} }-1} = x ^{ \frac{1}{3} }+1$