+589 Find x+1/x if
\[3x+\frac{2}{x}-4=2(x+9)-\left(7-\frac{1}{x}\right).\]
+357 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!
+2668 \(3x+\frac{2}{x}-4=2(x+9)-(7-\frac{1}{x})\)
\(3x+\frac{2}{x}-4=2x + 18-7+\frac{1}{x}\)
\(3x + {1 \over x} - 4 = 2x + 11\)
\(x + {1 \over x} - 4 = 11\)
\(x + {1 \over x} = \color{brown}\boxed{15}\)
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