Сократите дробь : x^2+x-6(дробьная Черта) x^2-2x-15

[latex] \frac{x^2+x-6 }{x^2-2x-15} = \frac{x^2 +3x-2x-2*3}{x^2+3x-5x-5*3} = \\ \\ = \frac{x(x+3) -2(x+3)}{x(x+3) -5*(x+3) } = \frac{(x-2)(x+3)}{(x-5)(x+3)} = \\ \\ = \frac{x-2}{x-5} [/latex]

[latex] x^{2}+x-6=0 [/latex] D=b²-4ac=1+24=25=5² x1=[latex] \frac{-1+5}{2}=2 [/latex] x2=[latex] \frac{1-5}{2}=-3 [/latex] [latex] x^{2}+x-6= [/latex](x-2)(x+3) [latex] x^{2} -2x-15 d=4+60=64=8 ^{2} [/latex] x1=[latex] \frac{2-8}{2} =-3 [/latex] x2=[latex] \frac{2+8}{2} =5[/latex] [latex] x^{2} -2x-15=(x+3)(x-5)[/latex] [latex] \frac{(x-2)(x+3)}{(x+3)(x-5)}= \frac{x-2}{x-5} [/latex]