(х-2)\(х+3)-30\(х^2-9)=3 решите уравнение .

ОДЗ
 x ≠ 3; x ≠ - 3

(x - 2)(x - 3) - 30 = 3(x - 3)(x + 3)
x^2 - 5x + 6 - 30 = 3(x^2 - 9)
x^2 - 5x - 24 = 3x^2 - 27
x^2 - 5x - 24 - 3x^2 + 27 = 0 
- 2x^2 - 5x + 3 = 0 
2x^2 + 5x - 3 = 0 
D = 25 + 24 = 49 = 7²
x₁ = ( - 5 + 7)/4 = 0,5;
x₂ = ( - 5 - 7)/4 = - 3 ==> x ≠ - 3;

ответ:
0,5

(x-2)/(x+3)-30/(x^2-9) = 3

x ∈ ( - ∞, - 3 ) U ( - 3, 3 ) U (3, ∞ )

x - 8/ x - 3 = 3/1 =>  ( x - 8 ) * 1 = ( x - 3 ) * 3 

1/2

x = 1/2