Question

1. Amplificati cu x-2 raportul 2x+1/x , unde x apartie R/{0.2}

2.Aduceti la acelasi numitor rapoartele x^2/x+1 si x/x^2-1 unde x apartine R/{-1,1}

3. Simplificati prin x raportul : x^2+x / x+x+x , unde x apartine lui R nenul

4. Simplificati prin x+3 raportul x^2+5x+6/x^2-9, unde x apartine lui R /{-3 , 3}

Answer 1

1. (2x+1)/x ×(x-2)=(2x²-x-4x-2)/x=(2x²-5x-2)/x

2. x²/(x+1) =x²(x-1)/(x+1)(x-1)
    x/(x²-1)=x/(x-1)(x+1)

3.  (x²+x) /( x+x+x)=x(x+1) /3x=(x+1) /3

4.  (x²+5x+6)/(x²-9)=(x²+3x+2x+6)/(x-3)(x+3)=[x(x+3)+2(x+3)]/(x-3)(x+3)=
=(x+3)(x+2)/(x-3)(x+3)=(x+2)/(x-3)