Выражение: (15x + 5x) : 3x - 8 + 30x (x-3 x^2-6x+9) 9-x^2 x-3

Решение во вложении:

((15х/(х-3))+(5х/(х²-6х+9))):((3х-8)/(9-х²))+(30х/(х-3))=-5х

1) (15х/(х-3))+(5х/(х²-6х+9))=((15х*(х-3)+5х)/(х-3)²=((15х²-45х+5х)/(х-3)²=

(15х²-40х)/(х-3)²=5х*(3х-8)/(х-3)²;

2) 5х*(3х-8)/(х-3)²:((3х-8)/(9-х²))=(5х*(3х-8)/(х-3)²)*((9-х²)/(3х-8))=(9-х²)*5х/(х-3)²)=

((3-х)(3+х)*5х)/(х-3)²)=-5х*(х+3)/(х-3);

3) -5х*(х+3)/(х-3)+30х/(х-3)=(-5х²-15х+30х)/(х-3)=(15х-5х²)/(х-3)=-5х(х-3)/(х-3)=

-5х