Răspuns: x²-5x+3x-15= x(x-5)+3 (X-5)=(x-5)(X+3) ; x²+7x+3x+21=x(x+7)+3(x+7)=(x+7)(x+3)
-5×3=-15 ;3-5=-2 ;x²-2x-15=(x+3)(x-5) ; 3×7=21 ; 3+7=10 ; x²+1ox+21= (x+3)(x+7) ; (x+3)(x-5)/(x+3)(x+7)=(x-5)/(x+7)
Explicație pas cu pas:
[tex]\it \dfrac{x^2-2x-15}{x^2+10x+21}=\dfrac{x^2+3x-5x-15}{x^2+3x+7x+21}=\dfrac{x(x+3)-5(x+3)}{x(x+3)+7(x+3)}=\dfrac{(x+3)(x-5)}{(x+3)(x+7)}=\\ \\ \\ =\dfrac{x-5}{x+7}[/tex]
