Question

Cократите дробь 1)5a+10/2a^2+13a+18 2)y^2-5y-36/81-y^2

Answer 1

1)5a+10/(2a^2+13a+18)

  2a^2+13a+18=2(a+2)(a+4,5)

D=169-4*2*18=25

a1=-2,  a2=-4,5

5a+10/(2a^2+13a+18)=5(a+2)/(2(a+2)(a+4,5))=5/(2a+9)

2)(y^2-5y-36)/(81-y^2)

y^2-5y-36=(y-9)(y+4)

D=25-4*1*(-36)=169

y1=9,    y2=-4

(y^2-5y-36)/(81-y^2)=(y-9)(y+4)/((9-y)(9+y)=-(9-y)(y+4)/((9-y)(9+y))=-(y+4)/(9+y)