If $x + \frac{1}{x} = 5, $ then the value of $\frac{3x}{2x^2+2-5x}$ will be ____________.
Answer & explanation
Correct answer: option 3
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,
$\frac{3x}{2x^2+2-5x}$ = $\frac{3x}{10x-5x}$ = \(\frac{3}{5}\)