We are given the expression:

$\frac{-y + 6}{y(-y + 3)}$

and need to evaluate it for $y = 3.2$. Here's the step-by-step process:

Step 1: Substitute $y = 3.2$ into the expression

$\frac{-3.2 + 6}{3.2(-3.2 + 3)}$

Step 2: Simplify the numerator

$-3.2 + 6 = 2.8$

Step 3: Simplify the denominator

$3.2(-3.2 + 3) = 3.2(-0.2) = -0.64$

Step 4: Divide the numerator by the denominator

$\frac{2.8}{-0.64} = -4.375$

Final Answer:

$\boxed{-4.375}$

Do you want a detailed breakdown or further questions about this process?

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Relative Questions:

1. What are the key properties of fractions when simplifying complex expressions?
2. How does substituting a value into an equation help solve real-world problems?
3. What happens if the denominator in a fraction equals zero, and how do we handle that?
4. Can this expression be evaluated for any value of $y$? Why or why not?
5. How does the sign of the fraction change when both numerator and denominator are negative?

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Tip:

Always check the domain of the expression to ensure the denominator does not become zero for specific values of $y$.