Answer
$21\frac{1}{2}$
Work Step by Step
Substitute $-2$ to $x$ in the given expression to obtain:
$3x^2-5x+\frac{1}{x}
\\= 3(-2)^2 -5(-2) + \frac{1}{-2}
\\=3(4) +10 - \frac{1}{2}
\\=12+10-\frac{1}{2}
\\=22-\frac{1}{2}
\\=21\frac{1}{2}$