Question

Решить уравнение x^2/x-4=16/x-4

Answer 1

$frac{x^{2} }{x} -4= frac{16}{x} -4 / *x \ x^2-4x=16-4x \ x^2-4x+4x-16=0 \ x^2=16 \ x=+- sqrt{16} \ x=+-4$

Answer 2

$frac{ x^{2} }{x - 4} = frac{16}{x - 4}$
$frac{ x^{2} }{x - 4} - frac{16}{x - 4} = 0$
$frac{ x^{2}- 16 }{x - 4} = 0$
$frac{(x - 4)(x + 4)}{x - 4} = 0$
$x + 4 = 0$                   $x - 4 neq 0$
$x = - 4$                       $x neq 4$