Answer
$x=(-1+\sqrt {17})/8,(-1-\sqrt {17})/8$
Work Step by Step
$5x/(x-2) - (x+1)/x = 3/(x)(x-2)$
$(x-2)*5x/(x-2) - (x-2)*(x+1)/x = (x-2)*3/(x)(x-2)$
$5x - (x-2)(x+1)/x = 3/(x)$
$5x*x - x*(x-2)(x+1)/x = x*3/(x)$
$5x^2-(x-2)(x+1)=3$
$5x^2-(x*x+x*1+x*-2+1*-2)=3$
$5x^2-(x^2+x-2x-2)=3$
$5x^2-(x^2-x-2)=3$
$5x^2-x^2+x+2=3$
$4x^2+x+2=3$
$4x^2+x-1=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-1±\sqrt {1^2-4*4*-1})/2*4$
$x=(-1±\sqrt {1+16})/8$
$x=(-1±\sqrt {17})/8$
