Question

E(x)=(x+1+2\x-1)  ×  x²-2x+1\x³-x²+x-1
x fiind numar real si x≠1

Answer 1

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