Question

x/x-3 - 5/x+3 = 18/x2-9

Answer 1

ОДЗ
х-3=0
х=3
х+3=0
х=-3
x²-9=0
(x-3)(x+3)=0
x=3
x=-3

$frac{x}{x-3}- frac{5}{x+3}= frac{18}{(x+3)(x-3)}$
$frac{x(x+3)-5(x-3)}{(x-3)(x+3)}= frac{18}{(x+3)(x-3)}$
$frac{ x^{2} +3x-5x+15}{(x-3)(x+3)}= frac{18}{(x+3)(x-3)}$
$frac{ x^{2} -2x+15}{(x-3)(x+3)}= frac{18}{(x+3)(x-3)}$
x²-2x+15=18
x²-2x-3=0
D=4+4*3=16
x₁=(2-4)/2=-1
x₂=(2+4)/2=3