Question

E(x)=x²-9/x²-4x+3+x+2/x+1-x²+5x+2/x²-1=1, pt orice x € R\ {-1;1;3}

Answer 1

E(x)=(x²-9)/(x²-4x+3)+(x+2)/(x+1)-(x²+5x+2)/(x²-1)=1
x²-4x+3=x²-3x-x+3=x(x-3)-(x-3)=(x-3)(x-1)

E(x)=(x²-9)/(x²-4x+3)+(x+2)/(x+1)-(x²+5x+2)/(x²-1)=
=(x-3)(x+3)/(x-3)(x-1)+(x+2)/(x+1)-(x²+5x+2)/(x-1)(x+1)=
=(x+3)/(x-1)+(x+2)/(x+1)-(x²+5x+2)/(x-1)(x+1)=
=[(x+3)(x+1)+(x+2)(x-1)-(x²+5x+2)]/(x-1)(x+1)=
=(x²+3x+x+3+x²+2x-x-2-x²-5x-2)/(x-1)(x+1)=
=(x²-1)/(x-1)(x+1)=
=(x-1)(x+1)/(x-1)(x+1)=1