Question 163899
x/3=4/x+1

multiply this equation by x then we get:
{{{x^2/3 = 4 + x}}}

multiply it again by 3 the we get:
{{{x^2 = 12 + 3x}}}
<=> {{{x^2 - 3x - 12 = 0}}}
Use abc formula to get the answer:
{{{x1 = (-b + sqrt(b^2 - 4*a*c))/(2*a)}}}
{{{x1 = (-(-3) + sqrt((-3)^2 - 4*1*(-12)))/(2*1)}}}
{{{x1 = (3 + sqrt(9 + 48))/2}}}
{{{x1 = (3 + sqrt(57))/2}}}

{{{x2 = (-b - sqrt(b^2 - 4*a*c))/(2*a)}}}
{{{x2 = (-(-3) - sqrt((-3)^2 - 4*1*(-12)))/(2*1)}}}
{{{x2 = (3 - sqrt(9 + 48))/2}}}
{{{x2 = (3 - sqrt(57))/2}}}

so the answers are:
{{{x1 = (3 + sqrt(57))/2}}} and {{{x2 = (3 - sqrt(57))/2}}}