Question

34 балла
5/x2+3x-15/x2-3x=16/x
пж через дискриминант и чтобы понятно пжпжпжпжп

Answer 1

$\frac{5}{x^{2}+3x }-\frac{15}{x^{2}-3x}=\frac{16}{x}\\\\\frac{5}{x(x+3)}-\frac{15}{x(x-3)} -\frac{16}{x}=0\\\\\frac{5x-15-15x-45-16x^{2}+144 }{x(x+3)(x-3)}=0\\\\\frac{-16x^{2}-10x+84 }{x(x+3)(x-3)}=0\\\\\frac{8x^{2}+5x-42 }{x(x+3)(x-3)}=0\\\\8x^{2}+5x-42=0, \ x\neq 0 \ ; \ x\neq-3 \ ; \ x\neq 3\\\\D=5^{2}-4*8*(-42)=25+1344=37^{2} \\\\x_{1} =\frac{-5-37}{16}=-2,625\\\\x_{2}=\frac{-5+37}{16}=2\\\\Otvet:\boxed{-2,625 \ ; \ 2}$