The problem presented in the image is as follows:

$\frac{1}{u} + \frac{2}{5} = \frac{7}{u} - 25$

Steps to solve for $u$:

1. Move all terms with $u$ to one side: We subtract $\frac{7}{u}$ from both sides:

   $\frac{1}{u} - \frac{7}{u} + \frac{2}{5} = -25$

   Simplifying the terms with $u$:

   $\frac{1 - 7}{u} + \frac{2}{5} = -25$

   $\frac{-6}{u} + \frac{2}{5} = -25$

2. Isolate the term with $u$: Subtract $\frac{2}{5}$ from both sides:

   $\frac{-6}{u} = -25 - \frac{2}{5}$

   To combine these, express $-25$ as a fraction:

   $\frac{-6}{u} = \frac{-125}{5} - \frac{2}{5}$

   $\frac{-6}{u} = \frac{-127}{5}$

3. Solve for $u$: Cross-multiply to eliminate the fractions:

   $-6 \cdot 5 = u \cdot (-127)$

   $-30 = -127u$

   Divide by $-127$:

   $u = \frac{30}{127}$

Thus, the solution is:

$u = \frac{30}{127}$

Would you like more details on any step? Here are some relative questions for further exploration:

1. How do we handle equations with multiple fractions like this?
2. Could $u = 0$ be a solution in rational equations?
3. What if the denominators were different? How would that affect the solution process?
4. How does cross-multiplication work in rational equations?
5. What happens when there are no solutions to an equation like this?

Tip: When solving rational equations, it's helpful to eliminate the fractions by finding a common denominator or cross-multiplying directly!