https://file.aiquickdraw.com/mathbot/file/17261144390489uwwm2km.jpg

The equation in the image is:

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

### Solution:
1. Cross-multiply to eliminate the fractions:
   \[
   2(x + 1) = 5x
   \]
   
2. Distribute the 2 on the left side:
   \[
   2x + 2 = 5x
   \]
   
3. Move all terms involving \(x\) to one side:
   \[
   2 = 5x - 2x
   \]
   Simplifying:
   \[
   2 = 3x
   \]
   
4. Solve for \(x\):
   \[
   x = \frac{2}{3}
   \]

Thus, the solution is \(x = \frac{2}{3}\).

Would you like further details on any steps?

Here are 5 related questions you could explore:
1. What happens if we change the equation to \(\frac{3}{x} = \frac{6}{x+2}\)?
2. How do you check if the solution is correct by substituting \(x\) back into the equation?
3. What are the conditions under which a rational equation like this has no solution?
4. How would the solution change if there were additional terms, such as \(\frac{2}{x} + 1 = \frac{5}{x+1}\)?
5. How do you solve similar equations that involve quadratic expressions?

**Tip**: Always check for restrictions by ensuring the denominator does not equal zero, which could make the equation undefined!

Learn how to solve the rational equation 2/x = 5/(x+1) by cross-multiplying and simplifying. This step-by-step solution explains key algebraic concepts and techniques suitable for students in Grades 8-10.

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