Question

Se considera expresia E(x)= (x+1/2x+1)^-1 + (2/x+1 - 1/x+2) : x^2+x-6/x^2-4. Aratati ca E (x)=2

Answer 1

E(x)= [(x+1)/(2x+1)]⁻¹ + [2/(x+1) - 1/(x+2)] : (x²+x-6)/(x²-4). Aratati ca E (x)=2
E(x)= [(x+1)/(2x+1)]⁻¹ + [2/(x+1) - 1/(x+2)] : (x²+x-6)/(x²-4)=
x²+x-6=x²-2x+3x-6=x(x-2)+3(x-2)=(x-2)(x+3)
=(2x+1)/(x+1) + (2x+4-x-1)/(x+1)(x+2) ×(x-2)(x+2)/(x-2)(x+3)=
=(2x+1)/(x+1) + 1/(x+1) =
=(2x+1+1)/(x+1) =
=(2x+2)/(x+1) =
=2(x+1)/(x+1)=2