Question

Simplificati raportul R(x)= x² +7x +6 supra x² +2x+1 ,unde x ∈ R \ {-1}

Answer 1

$\rm R(x)= \frac{x^2+7x+6}{x^2+2x+1}= \frac{x^2+x+6x+6}{x^2+2\cdot x\cdot1+1^2}= \frac{(\not x+\not1)(x+6)}{(x+1)^\not2}=\bold{ \frac{x+6}{x+1} }$

Answer 2

    
$R(x)= \frac{ x^{2} +7x+6}{ x^{2} +2x+1} = \\ \\ = \frac{ x^{2} +x+6x+6}{ x^{2} +x+x+1} = \\ \\ = \frac{ x(x +1)+6(x+1)}{ x(x +1)+(x+1)} = \\ \\ = \frac{ (x +1)(x+6)}{ (x +1)(x+1)} =\boxed{\frac{ (x+6)}{ (x+1)}}$