Question

Решите уравнение: б) 3/х^2+4х-15/х2-4х=4/х

Answer 1

$frac{3}{x^{2} +4x}-frac{15}{x^{2} -4x}=frac{4}{x}\\frac{3}{x(x+4)}-frac{15}{x(x-4)}-frac{4}{x}=0\\frac{3x-12-15x-60-4x^{2}+64 }{x(x-4)(x+4)}=0\\frac{4x^{2}+12x+8 }{x(x-4)(x+4)}=0\\frac{x^{2}+3x-2 }{x(x-4)(x+4)}=0\\left { {{x^{2}+3x+2=0 } atop {xneq0;xneq-4;xneq4}} right.\\D=(-3)^{2}-4*(2)=9-8=1\\x_{1}=frac{-3+1 }{2}=-1\\x_{2}=frac{-3-1 }{2}=-2$