https://file.aiquickdraw.com/mathbot/file/17274475746950dthz1db.jpg

The image shows a mathematical expression:

\[
\frac{3}{2}(1 + X) - \frac{1}{2}(1 + X)
\]

### Solution:

1. Apply the distributive property to both terms:
   \[
   \frac{3}{2}(1 + X) = \frac{3}{2} \cdot 1 + \frac{3}{2} \cdot X = \frac{3}{2} + \frac{3}{2}X
   \]
   \[
   \frac{1}{2}(1 + X) = \frac{1}{2} \cdot 1 + \frac{1}{2} \cdot X = \frac{1}{2} + \frac{1}{2}X
   \]

2. Subtract the second term from the first:
   \[
   \left( \frac{3}{2} + \frac{3}{2}X \right) - \left( \frac{1}{2} + \frac{1}{2}X \right)
   \]

3. Simplify by subtracting the constants and the terms with \(X\):
   \[
   \left( \frac{3}{2} - \frac{1}{2} \right) + \left( \frac{3}{2}X - \frac{1}{2}X \right) = 1 + X
   \]

So, the simplified expression is:

\[
1 + X
\]

Would you like more details or have any further questions? Here are some related questions for practice:

1. What happens if the coefficients were different in the original equation?
2. How would you simplify if the fraction coefficients were negative?
3. Can you solve similar expressions with higher powers of \(X\)?
4. What if there was another variable in the equation, like \(Y\)?
5. How would this problem change if it involved solving for \(X\)?

**Tip:** When simplifying expressions, always distribute the coefficients before combining like terms.

Simplify the expression (1 + X)^(3/2) - (1 + X)^(1/2)

Learn how to simplify the expression (1 + X)^(3/2) - (1 + X)^(1/2) using the distributive property and rules for exponents. Suitable for students in Grades 10-12.

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