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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.
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