The equation to solve from the image is:

$\frac{5}{r - 10} = \frac{7}{r + 10}$

Let's solve it step by step.

Step 1: Cross-multiply

$5(r + 10) = 7(r - 10)$

Step 2: Expand both sides

$5r + 50 = 7r - 70$

Step 3: Rearrange the equation to move terms involving $r$ to one side

$5r - 7r = -70 - 50$

$-2r = -120$

Step 4: Solve for $r$

$r = \frac{-120}{-2} = 60$

Thus, the solution is:

$r = 60$

Would you like more details on the steps?

Here are some related questions:

1. What happens when the denominators have common factors?
2. How would the solution change if we had negative coefficients?
3. Can this method be extended to quadratic equations?
4. How do we handle solutions that result in undefined values?
5. How would the equation change if one fraction had a different constant numerator?

Tip: Always check your solutions by substituting them back into the original equation to avoid extraneous solutions caused by restrictions in the domain (like dividing by zero).