Сократите дробь [latex] \frac{ x^{3}+5 x^{2} -4x-20 }{ x^{2} +3x-10} [/latex]

Если [latex]x \neq 2[/latex] и [latex]x \neq -5[/latex], то: [latex] \frac{x^3+5x^2-4x-20}{x^2+3x-10}= \frac{x^2*x+x^2*5+(-4)*x+(-4)*5}{x^2+5x-2x-10}= [/latex] [latex]= \frac{x^2+(x+5)+(-4)*(x+5)}{x*x+x*5+(-2)*x+(-2)*5} = \frac{[x^2+(-4)]*(x+5)}{x*(x+5)+(-2)*(x+5)} = \frac{(x^2-4)(x+5)}{[x+(-2)]*(x+5)}= [/latex] [latex]= \frac{(x^2-2^2)(x+5)}{(x-2)(x+5)}=\frac{(x-2)(x+2)*(x+5)}{(x-2)(x+5)*1}= \frac{x+5}{1}=x+5 [/latex]