Question

Упростите выражжение: $( frac{x-1}{x frac{1}{3}-1 } +x frac{1}{3} )* frac{x frac{1}{3} -1}{x frac{2}{3} -1}$

Answer 1

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