Question 83162
x + 1/x = 3/x + 3

Multiply each individual term by x, we get

x * x + (1/x) *x = (3/x) *x + 3 *x

x^2+ 1 = 3 + 3x

Get all the terms to one side, we get

x^2 -3x-3 +1 =0

x^2 -3x -2 = 0
It is of the form ax^2+ bx +c =0
Where a =1, b =-3, c =-2

Now substitute in the equation to get roots.
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (-(-3) +- sqrt( (-3)^2-4*1*-2 ))/(2*1) }}} 

{{{x = (3 +- sqrt( 9 + 8 ))/(2) }}} 


{{{x = (3 +- sqrt( 17 ))/(2) }}}