Сократите дробь х^3-х^2-х+1/х^4-2х^2+1

Question

Сократите дробь х^3-х^2-х+1/х^4-2х^2+1

Answer 1

X^3 - x^2 - x + 1 = x^2( x - 1 ) - ( x - 1 ) = ( x - 1 )( x^2 - 1 ) = ( x - 1 )( x - 1 )( x + 1 ) 
x^4 - 2x^2 + 1 = ( x^2 - 1 )^2 = ( x^2 - 1 )( x^2 + 1 )( x^2 - 1 )( x^2 + 1 ) =
= ( x - 1 )( x + 1 )( x - 1 )( x + 1 )( x^2 + 1 )^2 
3) ( ( x - 1)( x - 1 )( x + 1 )) / ( ( x - 1 )( x + 1 )( x - 1 )( x + 1 )( x^2 + 1 )^2 ) =
= ( x + 1 ) / ( x^2 + 1 )^2