Question

$\frac{3}{x {}^{2} + 4x} - \frac{15}{x {}^{2} - 4x } = \frac{4}{x}$
Решите дробно рациональное уравнение:​

Answer 1

Ответ:

Объяснение:

$\displaystyle\\\frac{3}{x {}^{2} + 4x} - \frac{15}{x {}^{2} - 4x } = \frac{4}{x}\\\\\\\frac{3}{x(x+4)}-\frac{15}{x(x-4)}=\frac{4}{x} \\\\\\x\neq  0;x\neq -4;x\neq 4\\\\3(x-4)-15(x+4)=4(x-4)(x+4)\\\\3x-12-15x-60=4(x^2-16)\\\\-12x-72=4x^2-64\\\\4x^2+12x+8=0\\\\x^2+3x+2=0\\\\x^2+x+2x+2=0\\\\x(x+1)+2(x+1)=0\\\\(x+1)(x+2)=0\\\\x=-2; x=-1\\\\Otvet:\{-2;-1\}$