Answer
$x=\frac{2}{3}$ or $x=5$
Work Step by Step
We simplify as follows:
$\frac{5}{x}+\frac{6}{x-2}=3$
$\frac{5x(x-2)}{x}+\frac{6x(x-2)}{x-2}=3x(x-2)$
$5(x-2)+6x=3x(x-2)$
$11x-10=3x^{2}-6x$
$3x^{2}-17x+10=0$
$(3x-2)(x-5)=0$
$3x-2=0$ or $x-5=0$
$3x=2$ or $x=5$
$x=\frac{2}{3}$ or $x=5$
