We need to solve the equation:

\[
\frac{2}{x} = \frac{5}{x} + 1
\]

### Step 1: Eliminate the denominators by multiplying through by \(x\) (assuming \(x \neq 0\)):

\[
2 = 5 + x
\]

### Step 2: Isolate \(x\) on one side of the equation:

\[
2 - 5 = x
\]

\[
x = -3
\]

Thus, the solution is:

\[
x = -3
\]

Would you like more details on any specific step?

Here are five related questions for further practice:
1. Solve \(\frac{3}{x} = \frac{7}{x} + 2\).
2. Solve \(\frac{1}{x} + \frac{4}{x} = 6\).
3. What is the solution to \(\frac{5}{x+1} = \frac{3}{x+1} + 2\)?
4. Solve \( \frac{7}{x} - \frac{2}{x} = 4\).
5. What happens if \(x = 0\) in a rational equation like this?

**Tip**: Always check for any restrictions on \(x\) when dealing with rational equations, such as \(x \neq 0\).

Learn how to solve the rational equation 2/x = 5/x + 1 through step-by-step instructions. This problem covers core algebraic concepts such as rational equations and equation balancing. Suitable for students in Grades 8-10.

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