Answer
$x=\frac{1+\sqrt {13}}{2},\frac{1-\sqrt {13}}{2}$
Work Step by Step
$\frac{2x}{x-1} - \frac{x+2}{x} = \frac{5}{x(x-1)}$
$x*(x-1)*\frac{2x}{x-1} - x*(x-1)*\frac{x+2}{x} = x*(x-1)*\frac{5}{x(x-1)}$
$x*2x-(x-1)(x+2)=5$
$2x^2-(x*x+x*2+x(-1)+2*(-1))=5$
$2x^2-(x^2+2x-x-2)=5$
$2x^2-x^2-2x+x+2=5$
$x^2-x+2=5$
$x^2-x-3=0$
$x=(-b±\sqrt{b^2-4ac})/2a$
$x=(-(-1)±\sqrt{(-1)^2-4*1*(-3)})/2*1$
$x=(1±\sqrt{1+12})/2$
$x=(1±\sqrt{13})/2$
Neither solution of $x$ will make the denominator negative.
