Question

Решите уравнение x/x+4+4/x-4=20/x^2-16

Answer 1

$\frac{x}{x+4} +\frac{4}{x-4} =\frac{20}{x^{2} -16}, x\neq -4, x\neq4  \\ \frac{x}{x+4}+\frac{4}{x-4}  - \frac{20}{x^{2} -16} = 0\\ \frac{x}{x+4} + \frac{4}{x-4} -\frac{20}{(x-4)(x+4)} =0\\ \frac{x(x-4)+4(x+4)-20}{(x-4)(x+4)}=0\\  x(x-4)+4(x+4)-20=0\\ x(x-4)+4(x+4)=20\\ x^{2} -4x+4x+16=20\\ x^{2} +16=20\\ x^{2} =20-16\\ x^{2} =4\\ x=+-2\\ \left \{ {{x=-2} \atop {x=2}} \right. , x\neq -4, x\neq 4\\ \left \{ {{x=-2} \atop {x=2}} \right.$