Question 764517
{{{ 6/x + 8/(x+5) = 3 }}}
Multiply both sides by {{{ x*( x+5 ) }}}
{{{ 6*( x+5 ) + 8x = 3x*( x+5 ) }}}
{{{ 6x + 30 + 8x = 3x^2 + 15x }}}
{{{ 14x + 30 = 3x^2 + 15x }}}
{{{ 3x^2 + x - 30 = 0 }}}
use quadratic formula
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}} 
{{{ a = 3 }}}
{{{ b = 1 }}}
{{{ c = -30 }}}
{{{ x = (-1 +- sqrt( 1^2 - 4*3*(-30) )) / (2*3) }}} 
{{{ x = (-1 +- sqrt( 1 + 360 )) / 6 }}} 
{{{ x = (-1 +- sqrt( 361 )) / 6 }}} 
{{{ x = (-1 + 19 ) / 6 }}} 
{{{ x = 18/6 }}}
{{{ x = 3 }}}
and, also
{{{ x = (-1 - 19 ) / 6 }}} 
{{{ x = -20/6 }}}
{{{ x = -10/3 }}}
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check:
{{{ ( x - 3 )*( x + 10/3 ) = 0 }}}
{{{ x^2 - 3x + (10/3)*x - 10 = 0 }}}
{{{ x^2 - (9/3)*x + (10/3)*x - 10 = 0 }}}
{{{ x^2 + (1/3)*x - 10 = 0 }}}
{{{ 3x^2 + x - 30 = 0 }}}
OK