Question

x+4/x-4-x-4/x+4=1-x²/x²-16

Answer 1

$\frac{x+4}{x-4} - \frac{x-4}{x+4} = \frac{1-x^2}{x^2-16} \\ \\ \frac{(x+4)^2 - (x-4)^2}{(x-4)(x+4)} = \frac{1-x^2}{x^2-16} \\ \\ \frac{16x}{x^2-16} = \frac{1-x^2}{x^2-16} \\ \\ x^2-16\ =\ 0\ \ \ OR\ \ 16x = 1-x^2 \\ \\ Either\ \ x = +4\ \ -4\ \ \ \ OR\ \ \ x^2+16x-1=0 \\ \\ x = +4,\ -4,\ \ or\ x=-8-\sqrt{65},\ \ OR\ -8+\sqrt{65}$