Сократите дробь:
1) (x+4)/(x^2+5x+4)
2) (x^2-4)/(x^2-5x+6)
3) (a^2+5a+6)/(a^2+6a+9)
1) (x+4)/(x^2+5x+4)
2) (x^2-4)/(x^2-5x+6)
3) (a^2+5a+6)/(a^2+6a+9)
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Answers & Comments
x^2+5x+4=0
D=25-4*1*4=9
x₁=(-5-3)/2=-4
x₂=(-5+3)/2=-1
(x+4)/((x+4)(x+1))=1/x+1
2)(x^2-4)/(x^2-5x+6)=((x-2)(x+2))/(x^2-5x+6)
x^2-5x+6=0
D=25-4*1*6=1
x₁=(5-1)/2=2
x₂=(5+1)/2=3
((x-2)(x+2))/((x-2)(x-3)=(x+2)/(x-3)
3)(a^2+5a+6)/(a^2+6a+9)
a^2+5a+6=0
D=25-4*1*6=1
a₁=(-5-1)/2=-3
a₂=(-5+1)/2=-2
a^2+6a+9=0
D=36-4*1*9=0
a=-6/2=-3
((a+3)(a+2))/(a+3)=a+2