The image shows the following expression to solve:

$\frac{4}{7} - \frac{5}{21} + \frac{9}{14}$

Steps to solve:

1. Find the Least Common Denominator (LCD): The denominators are 7, 21, and 14. The least common denominator of these is 42.

2. Convert each fraction to have the denominator of 42: $\frac{4}{7} = \frac{4 \times 6}{7 \times 6} = \frac{24}{42}$ $\frac{5}{21} = \frac{5 \times 2}{21 \times 2} = \frac{10}{42}$ $\frac{9}{14} = \frac{9 \times 3}{14 \times 3} = \frac{27}{42}$

3. Perform the indicated operations: Now the expression becomes: $\frac{24}{42} - \frac{10}{42} + \frac{27}{42}$

   Combine the numerators: $24 - 10 + 27 = 41$

   So, the result is: $\frac{41}{42}$

Thus, the simplified answer is $\frac{41}{42}$.

Would you like more details on any step?

Here are 5 related questions to expand on this topic:

1. How do you find the least common denominator for three fractions?
2. How can you add or subtract fractions with different denominators?
3. What happens when the numerator is larger than the denominator?
4. Can you always simplify fractions before adding or subtracting them?
5. What are some common mistakes when working with fractions?

Tip: Always double-check your least common denominator to ensure accurate addition or subtraction of fractions.