Given the values \( x = \frac{1}{3} \) and \( y = \frac{4}{3} \), you want to evaluate the expression \( y - \frac{-xy + y^2}{x - y} \).

### Step 1: Substitute the values into the expression
Substitute \( x = \frac{1}{3} \) and \( y = \frac{4}{3} \) into the expression:
\[
y - \frac{-xy + y^2}{x - y} = \frac{4}{3} - \frac{-\left(\frac{1}{3}\right)\left(\frac{4}{3}\right) + \left(\frac{4}{3}\right)^2}{\frac{1}{3} - \frac{4}{3}}
\]

### Step 2: Simplify the numerator
First, calculate \(-xy\) and \(y^2\):
\[
-xy = -\left(\frac{1}{3}\right)\left(\frac{4}{3}\right) = -\frac{4}{9}
\]
\[
y^2 = \left(\frac{4}{3}\right)^2 = \frac{16}{9}
\]
So, the numerator becomes:
\[
-\frac{4}{9} + \frac{16}{9} = \frac{12}{9} = \frac{4}{3}
\]

### Step 3: Simplify the denominator
Now, calculate \(x - y\):
\[
x - y = \frac{1}{3} - \frac{4}{3} = -\frac{3}{3} = -1
\]

### Step 4: Simplify the entire fraction
Now substitute back into the fraction:
\[
\frac{4}{3} - \frac{\frac{4}{3}}{-1} = \frac{4}{3} + \frac{4}{3}
\]

### Step 5: Final simplification
Add the two fractions:
\[
\frac{4}{3} + \frac{4}{3} = \frac{8}{3}
\]

So, the final value of the expression is \(\frac{8}{3}\).

Would you like to discuss any specific part of this calculation or have any questions?

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Here are 5 related questions to consider:
1. How does the expression change if \( x \) and \( y \) have different signs?
2. What is the result if \( x \) and \( y \) are both negative?
3. How would the calculation change if the numerator was a more complex polynomial?
4. Can you generalize the solution for any \( x \) and \( y \)?
5. What happens to the expression if \( y = 0 \)?

**Tip:** When working with fractions, it's often easier to simplify the expression step by step, especially when dealing with negative signs.

Learn how to evaluate the expression y - (-xy + y^2)/(x - y) with x = 1/3 and y = 4/3. This problem involves fraction operations and algebraic simplification steps. Suitable for students in Grades 7-9.

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