Question

(x²-4分之x²+x+1)²÷(x三次方-3x²+2x÷x三次方)²

Answer 1

[(x²-4)/(x²+x+1)]²÷[(x³-3x²+2x)÷x³]²×[x÷(x+2)]²

=[(x²-4)/(x²+x+1)]²÷[(x²-3x+2)÷x²]²×[x÷(x+2)]²

=[(x²-4)/(x²+x+1)]²×[x²/(x²-3x+2)]²×[x÷(x+2)]²

=[(x+2)(x-2)/(x²+x+1)×x²/(x-2)(x-1)×x/(x+2)]²

=[x³/(x²+x+1)(x-1)]²

=[x³/(x³-1)]²