Question

Va rog faceti-mi si mie acest E(x) ,scuzati calitatea foografiei

Answer 1

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