finding solution to 1 + 1/x^2 = 3/x?

when we have fraction in the equation.

We can always multiply the least common denominator on each term.

lcd between x and x^2 is x^2 obviously .
le'ts multiply each term by x^2

then it will come out

x^2 + 1 = 3x ( make it = 0 )
x^2 - 3x + 1 = 0 ( no way to factor it, use quadratic formula )

x = - b +/- sqrt ( b^2 - 4ac ) / 2a
x = 3 +/- sqrt ( 9 - 4 ) / 2
x = [3 + sqrt(5) ]/2 or [3 - sqrt ( 5) ]/2

x ² + 1 = 3 x
x ² - 3 x + 1 = 0
x = [ 3 ± √ (9 - 4) ] / 2
x = [ 3 ± √ 5 ] / 2

PS
Does not factorise.

x^2-3x+1 = 0 --->x = (3+sqrt5)/2 and (3-sqrt5)/2