преобразуйте в алгебраическую дробь рациональное выражение 2/x-3 - 18x/x в кубе - 27 - x-3/x в квадрате +3x+9 и найдите значение полученной дроби при а)x=0 б) x=3
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2/(х-3) - 18х/(х³-27) - (х-3)/(х²+3х+9) =
= 2/(х-3) - 18х/(х-3)(х²+3х+9) - (х-3)/(х²+3х+9) =
= 2(х²+3х+9)/(х-3)(х²+3х+9) - 18х/(х-3)(х²+3х+9) - (х-3)(х-3)/(х-3)(х²+3х+9) =
= (2х²+6х+18)/(х-3)(х²+3х+9) - 18х/(х-3)(х²+3х+9) - (х²-6х+9)/(х-3)(х²+3х+9) =
= (2х²+6х+18 - 18х - х²+6х-9)/(х-3)(х²+3х+9) =
= (х²-6х+9)/(х-3)(х²+3х+9) =
= (х-3)² / (х-3)(х²+3х+9) =
= (х-3) / (х²+3х+9),
а)
при x = 0: (0-3) / (0²+3*0+9) = -3/9 = -1/3,
б)
при x = 3: (3-3) / (3²+3*3+9) = 0/27 = 0