Question

Помогите срочно рівняння

Answer 1

$\frac{14}{x^{2}-9 }+\frac{2}{3x-9}=2\frac{2}{3}\\\\\frac{14}{(x-3)(x+3)}+\frac{2}{3(x-3)}-\frac{8}{3}}=0\\\\\frac{14*3+2*(x+3)-8(x^{2}-9) }{3(x-3)(x+3)} =0\\\\\frac{42+2x+6-8x^{2}+72 }{3(x-3)(x+3)}=0\\\\\frac{8x^{2}-2x-120 }{3(x-3)(x+3)}=0\\\\\left \{ {{8x^{2}-2x-120=0 } \atop {x-3\neq0;x+3\neq0}} \right.\\\\\left \{ {{4x^{2}-x-60=0 } \atop {x\neq3;x\neq-3}} \right.$

$4x^{2} -x-60=0\\\\D=(-1)^{2}-4*4*(-60)=1+960=961=31^{2}\\\\x_{1} =\frac{1+31}{8}=\frac{32}{8}=4\\\\x_{2}=\frac{1-31}{8}=-\frac{30}{8}=-3,75\\\\Otvet:\boxed{-3,75;4}$