Question

Математика, помогите

Answer 1

$\frac{ x^{4}-2 x^{3}+2x -1}{ x^{4}-2 x^{3} +2 x^{2} -2x+1 }( x^{2} +1)= \\ \frac{( x^{4}-1)-2x( x^{2} -1) }{ x^{4}-2 x^{3} + x^{2} + x^{2} -2x+1 }( x^{2} +1)= \\ \frac{( x^{2} -1)( x^{2} +1)-2x( x^{2} -1)}{ x^{2} ( x^{2} -2x+1)+( x^{2} -2x+1)}( x^{2} +1)= \\ \frac{( x^{2} -1)( x^{2} -2x+1)}{( x^{2} -2x+1)( x^{2} +1)}( x^{2} +1)= \\ ( x^{2} -1)=(x-1)(x+1)$