$\frac{x}{x-2}+\frac{2}{x}=\frac{5}{x}$

Step 1 ：We are given the rational equation \(\frac{x}{x-2} + \frac{2}{x} = \frac{5}{x}\).

Step 2 ：To solve this, we first need to clear the fractions by multiplying each term by the least common denominator (LCD) of all the fractions. The LCD of \(x\), \(x-2\), and \(x\) is \(x(x-2)\).

Step 3 ：After clearing the fractions, we get the equation \(x(x - 2)(\frac{x}{x - 2} + \frac{2}{x}) = 5x - 10\).

Step 4 ：Solving this equation gives us the solutions \(\frac{3}{2} - \frac{\sqrt{15}i}{2}\) and \(\frac{3}{2} + \frac{\sqrt{15}i}{2}\).

Step 5 ：These solutions are complex numbers, which means that there are no real solutions to the equation.

Step 6 ：\(\boxed{\text{The equation } \frac{x}{x-2} + \frac{2}{x} = \frac{5}{x} \text{ has no real solutions.}}\)