Question 263102
{{{(x + 2/x)/(3 + 4/x) = 5x}}}
Multiply both sides by {{{3 + 4/x}}}
{{{x + 2/x = 5x*(3 + 4/x)}}}
{{{x + 2/x = 15x + 20}}}
Multiply both sides by {{{x}}}
{{{x^2 + 2 = 15x^2 + 20x}}}
{{{14x^2 + 20x - 2 = 0}}}
{{{7x^2 + 10x - 1 = 0}}}
Solve using quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 7}}}
{{{b = 10}}}
{{{c = -1}}}
{{{x = (-10 +- sqrt( 10^2-4*7*(-1) ))/(2*7) }}}
{{{x = (-10 +- sqrt( 100 + 28 ))/14 }}}
{{{x = (-10 + 8*sqrt(2))/14}}}
(1) {{{x = (-5 + 4*sqrt(2))/7}}}
and
(2) {{{x = (-5 - 4*sqrt(2))/7}}}
You can check the 2 answers by plugging each back into equation