$$3x+\frac{2}{x}-4=2(x+9)-\left(7-\frac{1}{x}\right).$$

3x+2/x-4=2x+18-7+1/x

3x+2/x-4=2x+1/x+11

3x+2/x+7=2x+1/x

3x+1/x+7=2x

[(3x+1/x+8)/2]/(3x+1/x+7)/2

This simplifies down to 

(3x^2+8x+1)/(3x^2+7x+1)

Yay!

$3x+\frac{2}{x}-4=2(x+9)-(7-\frac{1}{x})$

$3x+\frac{2}{x}-4=2x + 18-7+\frac{1}{x}$

$3x + {1 \over x} - 4 = 2x + 11$

$x + {1 \over x} - 4 = 11$

$x + {1 \over x} = \color{brown}\boxed{15}$