Let's solve the equation shown in the image:

The equation is:

$\frac{4}{5} + \frac{5}{1 - \frac{1}{3}} = \, ?$

Step-by-step solution:

1. Simplify the denominator in the second term: $1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$

   So the second term becomes: $\frac{5}{\frac{2}{3}}$

2. Simplify the fraction division: Dividing by a fraction is equivalent to multiplying by its reciprocal: $\frac{5}{\frac{2}{3}} = 5 \cdot \frac{3}{2} = \frac{15}{2}$

3. Combine the terms: Now the equation becomes: $\frac{4}{5} + \frac{15}{2}$

4. Find a common denominator: The denominators are $5$ and $2$. The least common denominator (LCD) is $10$. Rewrite each fraction with a denominator of $10$: $\frac{4}{5} = \frac{8}{10}, \quad \frac{15}{2} = \frac{75}{10}$

5. Add the fractions: Add the numerators: $\frac{8}{10} + \frac{75}{10} = \frac{83}{10}$

6. Final answer: $\frac{83}{10} = 8.3$

Final Result:

The value of the expression is: $\boxed{8.3}$

Would you like me to go into more details about any step?

Related Questions:

1. How can fractions with different denominators be added together?
2. What are the rules for dividing fractions, and how do they apply here?
3. What is the concept of least common denominator (LCD)?
4. How can this calculation be expressed as a mixed number instead of a decimal?
5. Can this problem be solved faster with a calculator?

Tip:

When simplifying fractions, always work step-by-step and check each part carefully to avoid errors, especially when dealing with multiple operations.