Question 172130
{{{5/x + 7/6 = 4/(x-4)}}}
If you multiply each side by {{{6x*(x - 4)}}},
that will guarantee that no fractions will
be left
{{{5*6*(x - 4) + 7x*(x - 4) = 4*6*x}}}
{{{30*(x - 4) + 7x*(x - 4) = 24x}}}
{{{30x - 120 + 7x^2 - 28x = 24x}}}
{{{7x^2 - 22x - 120 = 0}}}
Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 7}}}
{{{b = -22}}}
{{{c = -120}}}
{{{x = (-(-22) +- sqrt( (-22)^2-4*7*(-120) ))/(2*7) }}}
{{{x = (22 +- sqrt( 484 + 3360 )) / 14 }}}
{{{x = (22 +- sqrt(3844)) / 14 }}} 
{{{x = (22 + 62) / 14 }}}
{{{x = 6}}}
and
{{{x = (22 - 62) / 14}}}
{{{x = -(20/7)}}}
I checked both answers, and they look right