algebra

$\frac{x+1}{x}=3$

$x+1=3x$

$1=2x$

$\frac{1}{2}=x$ or $x=\frac{1}{2}$

so:

$x^4 + \frac{1}{x^4}$

$(\frac{1}{2})^4 + (\frac{1}{(\frac{1}{2})^4})$

$0.0625+\frac{1}{0.0625}$

$16.0625$

Answer = 16.0625