https://file.aiquickdraw.com/mathbot/file/1729525556566ywdapf9m.jpg

The equation provided in the image is:

\[
\frac{4}{5}y - \left(-\frac{1}{5}y\right) + \frac{3}{2}y
\]

### Step-by-step simplification:
1. Distribute the negative sign:
\[
\frac{4}{5}y + \frac{1}{5}y + \frac{3}{2}y
\]

2. Now, combine the terms by getting a common denominator for the fractions.
   - For \(\frac{4}{5}y + \frac{1}{5}y\), since the denominators are the same, we can add the numerators:
   \[
   \frac{4 + 1}{5}y = \frac{5}{5}y = y
   \]

3. Now, the equation becomes:
\[
y + \frac{3}{2}y
\]

4. To combine these two terms, we need to express \(y\) with the same denominator as \(\frac{3}{2}y\). Recall that \(y = \frac{2}{2}y\), so the equation is now:
\[
\frac{2}{2}y + \frac{3}{2}y = \frac{2+3}{2}y = \frac{5}{2}y
\]

### Final Answer:
The simplified form of the expression is:

\[
\frac{5}{2}y
\]

Would you like a more detailed explanation or have any questions?

### Related Questions:
1. How do you combine like terms with different denominators?
2. How do you convert a fraction to have a common denominator?
3. What are some common mistakes to avoid when simplifying expressions with fractions?
4. How does distributing negative signs impact terms in an equation?
5. How can you factor out terms from an expression to simplify it?

### Tip:
When working with fractional coefficients, always look for common denominators to simplify addition or subtraction.

Simplify the expression: (4/5)y - (-1/5)y + (3/2)y

Learn how to simplify an algebraic expression involving fractions: (4/5)y - (-1/5)y + (3/2)y. This detailed step-by-step solution demonstrates how to combine like terms with different denominators. Suitable for middle school students.

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