To solve the equation \( \frac{N}{2} - \frac{3N}{4} + \frac{5N}{6} = 21 \), we first need to combine the terms involving \( N \). 

Here are the steps to solve it:

1. Find a common denominator for the fractions. The denominators are 2, 4, and 6. The least common multiple (LCM) of these numbers is 12.
   
2. Rewrite each term with the common denominator of 12:
   \[
   \frac{N}{2} = \frac{6N}{12}
   \]
   \[
   \frac{3N}{4} = \frac{9N}{12}
   \]
   \[
   \frac{5N}{6} = \frac{10N}{12}
   \]

3. Substitute these into the equation:
   \[
   \frac{6N}{12} - \frac{9N}{12} + \frac{10N}{12} = 21
   \]

4. Combine the fractions on the left side:
   \[
   \frac{6N - 9N + 10N}{12} = 21
   \]
   \[
   \frac{7N}{12} = 21
   \]

5. Solve for \( N \) by multiplying both sides by 12 to eliminate the fraction:
   \[
   7N = 21 \times 12
   \]
   \[
   7N = 252
   \]

6. Divide both sides by 7 to isolate \( N \):
   \[
   N = \frac{252}{7}
   \]
   \[
   N = 36
   \]

Thus, the solution to the equation is \( N = 36 \).

Would you like any details or have any questions? Here are five questions you might want to ask next:

1. How do you find the least common multiple of several numbers?
2. Can you explain how to simplify fractions?
3. What are other methods to solve equations with fractions?
4. How can I check if my solution to an equation is correct?
5. What are the applications of solving linear equations in real life?

**Tip:** When dealing with fractions in equations, always look for a common denominator to simplify the process of combining terms.

Learn how to solve the equation involving fractions: N/2 - 3N/4 + 5N/6 = 21. Follow a step-by-step solution combining terms, finding a common denominator, and isolating N. Suitable for high school students studying equations with fractions.

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