You've provided a photo of a rational equation to solve. Let's go through the solution step-by-step.

The equation given is: $\frac{3x - 1}{5} + \frac{2x - 1}{6} = \frac{5}{6}$

First, we need to find a common denominator for the fractions on the left side, which is 30. We can rewrite each fraction with this common denominator: $\frac{3x - 1}{5} = \frac{6(3x - 1)}{30}$ $\frac{2x - 1}{6} = \frac{5(2x - 1)}{30}$ $\frac{5}{6} = \frac{25}{30}$

Now, rewrite the equation: $\frac{18x - 6 + 10x - 5}{30} = \frac{25}{30}$

Combine like terms in the numerator: $\frac{28x - 11}{30} = \frac{25}{30}$

Since the denominators are the same, we can equate the numerators: $28x - 11 = 25$

Now, solve for $x$: $28x = 25 + 11$ $28x = 36$ $x = \frac{36}{28}$ $x = \frac{9}{7}$

Thus, $x = \frac{9}{7}$.

Do you want to explore further details or do you have any questions about the steps? Here are some questions you might consider:

1. How can you check if $\frac{9}{7}$ is indeed a correct solution to the equation?
2. What happens if you were to substitute different values for $x$ into the original equation?
3. What would be the graphical interpretation of this equation?
4. How would the solution change if the equation on the right was different, say $\frac{1}{2}$?
5. Are there scenarios where a rational equation like this would have no solution or infinite solutions?

Tip: Always simplify the fractions during your calculation to make calculations easier and avoid mistakes.