Question 34175
this has no solution, since {{{ 6/x + 18/ x+8 = 8}}} gives {{{ 6/x + 18/ x = 0}}} and then the x will ultimately become a zero.


Perhaps you meant to write {{{ 6/x + 18/(x+8) = 8 }}}? If so, we get


{{{ ((6(x+8))/(x(x+8))) + ((18x)/(x(x+8))) = 8 }}}
{{{ ((6(x+8)+18x)/(x(x+8))) = 8 }}}
{{{ 6(x+8)+18x = 8x(x+8) }}}
{{{ 6x+48+18x = 8x^2+64x }}}
{{{ 48+24x = 8x^2+64x }}}
{{{ 0 = 8x^2+40x-48 }}}
{{{ 8x^2+40x-48 = 0 }}}
{{{ x^2+5x-6 = 0 }}}
(x+6)(x-1) = 0


so, either x+6=0 or x-1=0
hence x=-6 or x=1


jon.