Решите уравнение x^2/x+4=4x/x+4

Question

Решите уравнение x^2/x+4=4x/x+4

Answer 1

4x(x + 4) =x^2(x + 4)
4x( x + 4) - x^2(x + 4) =0
( x + 4)(4x - x^2) = 0
x(4 - x)(x + 4) = 0
x( 4 - x)(4 + x) = 0
x( 16 - x^2) = 0
x = 0
16 - x^2 = 0
- x^2 = - 16
x^2 = 16
x = 4
x = - 4
Ответ: x1 = 0, x2 = 4, x3 = - 4.