Question

x+1/x-3+12/x+3=24/x2-9

Answer 1

$frac{x+1}{x-3}+frac{12}{x+3}=frac{24}{x^{2} -9}\\frac{x^{2}+3x+x+3+12x-36 }{(x-3)(x+3)}=frac{24}{x^{2}-9 }\\frac{x^{2}+16x-33 }{x^{2}-9 }=frac{24}{x^{2}-9 } \\left { {{x^{2}+16x-33=24 } atop {xneq-3;xneq 3 }} right.\\x^{2} +16x-57=0\\D=16^{2}-4*(-57)=256+228=484=22^{2}\\x_{1}=frac{-16+22}{2}=3\\x_{2}=frac{-16-22}{2}=-frac{38}{2}=-19$

Ответ : - 19