Question 591554
{{{ (10/x)+3=(x+9)/(x-4) }}}


{{{ (10/x)-((x+9)/(x-4)) =-3}}}


The LCD = x(x-4)

multiply equation by the LCD

10(x-4) -x(x+9) = -3x(x-4)


{{{10x-40-x^2-9x=-3x^2+12x}}}


{{{x-40-x^2=-3x^2+12x}}}


{{{3x^2-x^2+x-12x-40=0}}}


{{{2x^2-11x-40=0}}}


{{{2x^2-16x+5x-40=0}}}


{{{2x(x-8)+5(x-8)=0}}}

(x-8)(2x+5)=0


x= 8 Or x=  -5/2