Let’s simplify the expression:  
\[
\frac{3}{2}h + 3 - \frac{6}{5}h - 2
\]

### Step-by-Step Solution:

1. **Group like terms (terms with \(h\)):**
   \[
   \frac{3}{2}h - \frac{6}{5}h
   \]

2. **Group constant terms:**
   \[
   3 - 2
   \]

3. **Simplify constants:**
   \[
   3 - 2 = 1
   \]

4. **Simplify the \(h\)-terms:**

   To combine \(\frac{3}{2}h\) and \(-\frac{6}{5}h\), we need a common denominator:
   - The least common denominator of 2 and 5 is 10.
   - Rewrite the fractions:
     \[
     \frac{3}{2}h = \frac{15}{10}h, \quad \frac{6}{5}h = \frac{12}{10}h
     \]
   - Now, subtract:
     \[
     \frac{15}{10}h - \frac{12}{10}h = \frac{3}{10}h
     \]

5. **Combine everything:**

   Now, the expression becomes:
   \[
   \frac{3}{10}h + 1
   \]

### Final Answer:
\[
\frac{3}{10}h + 1
\]

---

Would you like to see more details or have any questions?  
Here are some related questions:  
1. How do you find the least common denominator for two fractions?  
2. How do you add or subtract fractions with different denominators?  
3. What is a like term, and how do you combine them?  
4. How does distributing and factoring differ from combining like terms?  
5. What happens if the variables involve exponents (e.g., \(h^2\) instead of \(h\))?

**Tip:** When working with algebraic fractions, always simplify step-by-step to avoid mistakes with signs and denominators.

Learn how to simplify the algebraic expression 3/2h + 3 - 6/5h - 2 using the method of combining like terms and fractions. This problem covers key algebraic concepts such as finding common denominators and working with linear expressions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation