Question

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

Answer 1

$frac{x}{x+4} +frac{4}{x-4} =frac{20}{x^{2} -16}, xneq -4, xneq4  \ frac{x}{x+4}+frac{4}{x-4}  - frac{20}{x^{2} -16} = 0\ frac{x}{x+4} + frac{4}{x-4} -frac{20}{(x-4)(x+4)} =0\ frac{x(x-4)+4(x+4)-20}{(x-4)(x+4)}=0\  x(x-4)+4(x+4)-20=0\ x(x-4)+4(x+4)=20\ x^{2} -4x+4x+16=20\ x^{2} +16=20\ x^{2} =20-16\ x^{2} =4\ x=+-2\ left { {{x=-2} atop {x=2}} right. , xneq -4, xneq 4\ left { {{x=-2} atop {x=2}} right.$