\(\frac{x}{x+1}+\frac{x+1}{x+2}+\frac{x+2}{x}=\frac{25}{6}\)
<=> 6x2(x + 2) + 6x(x + 1)2 + 6(x + 2)2(x + 1) = 25x(x + 1)(x + 2)
<=> 18x2 + 54x2 + 54x + 24 = 25x3 + 75x2 + 50x
<=> 18x2 + 54x2 + 54x + 24 - 25x2 - 75x2 - 50x = 0
<=> -7x3 - 21x2 + 4x + 24 = 0
<=> (-7x2 - 28x - 24)(x - 1) = 0
vì 7x2 + 28x + 24 khác 0 nên:
<=> x - 1 = 0
<=> x = 0