First combine terms. Then turn it into a quadratic equation by multiplying both sides by 4x.
2x + 1/x - 19/4 = 0
8x^2 - 19x + 4 = 0
Use the quadratic equation to find the rots. It does not appear to factor easily.
1/4 = 3 - 2x - 1/x + 2
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