Find the roots of $x\ -\ \frac{3}{x} \ =\ 2$.

Given: $x\ -\ \frac{3}{x} \ =\ 2$

To find: Here we have to find the roots of the given equation $x\ -\ \frac{3}{x} \ =\ 2$.

Solution:

$x\ -\ \frac{3}{x} \ =\ 2$

$\frac{x^{2} \ -\ 3}{x} \ =\ 2$

$x^{2} \ -\ 3\ =\ 2x$

$x^{2} \ -\ 2x\ -\ 3\ =\ 0$

$x^{2} \ -\ 3x\ +\ x\ -\ 3\ =\ 0$

$x( x\ -\ 3) \ +\ 1\ ( x\ -\ 3) \ =\ 0$

$( x\ -\ 3)( x\ +\ 1) \ =\ 0$

So,

$x\ -\ 3\ =\ 0$ and $x\ +\ 1\ =\ 0$

$\mathbf{x\ =\ 3}$  and  $\mathbf{x\ =\ -1}$

Therefore, the roots are 3 and $-$1.