If $x + \frac{1}{x} = 5, $ then the value of $\frac{3x}{2x^2+2-5x}$ will be ____________.

$\frac{3}{5}$

If $x + \frac{1}{x} = 5,$

then the value of $\frac{3x}{2x^2+2-5x}$

If $x + \frac{1}{x} = 5,$ then,

\(\frac{x^2 + 1}{x}\) = 5

$x^2 + 1$ = 5x

$2x^2 + 2$ = 10x

Put in the required equation,

$\frac{3x}{2x^2+2-5x}$ = $\frac{3x}{10x-5x}$ = \(\frac{3}{5}\)