Question

решите уравнение:

4/(x²+6x+9)+6/(9-x²)=1/(x-3)

Answer 1

4/(x^2+6x+9)+6/(9-x^2)=1/(x-3)

4/((x+3)(x+3))-6/((x-3)(x+3))-1/(x-3)=0

(4(x-3)-6(x+3)-(x+3)^2)/((x+3)^2(x-3))=0

(4(x-3)-6(x+3)-(x+3)^2)=0

4x-12-6x-18-x^2-6x-9=0

-x^2-8x-39=0

x^2+8x+39=0

D=b^2-4ac=-92

D<0 - уравнение не имеет решений

 

Answer 2

4/(x²+6x+9)+6/(9-x²)=1/(x-3)

$frac{4}{(x+3)^2}-frac{6}{(x-3)(x+3)}-frac{1}{x-3}=0$

4(x-3)-6(x+3)-(x+3)^2 = 0

4x-12-6x-18-x^2-6x-9=0

-x^2-8x-39=0

x^2 + 8x + 39 = 0   D<0    корней нет