Perform the indicated operations and simplify. (Enter any b values for which the equivalence does not hold as a comma-separated list. If there are no such b values, enter NONE.)

b+(1/b-4)-3

To simplify the expression \( b + \left(\frac{1}{b} - 4\right) - 3 \), we will follow these steps:

### 1. Simplify the parentheses:
\[
b + \left(\frac{1}{b} - 4\right) - 3 = b + \frac{1}{b} - 4 - 3
\]

### 2. Combine like terms:
\[
b + \frac{1}{b} - 7
\]

This is the simplified expression.

### Now, for the condition:
We must consider if there are any values of \( b \) that make the expression undefined. The only potential issue arises from the term \( \frac{1}{b} \), which is undefined when \( b = 0 \).

### Therefore, the expression is undefined when \( b = 0 \).

#### Answer:
The simplified expression is \( b + \frac{1}{b} - 7 \), and the value of \( b \) for which the equivalence does not hold is \( b = 0 \).

Would you like further details or have any questions?

### Relative Questions:
1. What happens when \( b = 0 \) in rational expressions?
2. How can you identify terms that make an expression undefined?
3. How would this expression change if it were a fraction instead of a sum?
4. How do parentheses affect the order of operations?
5. Can the expression be factored further if written in a different form?

**Tip:** Always check for values that make a denominator zero when simplifying expressions with fractions.

Perform the indicated operations and simplify. (Enter any b values for which the equivalence does not hold as a comma-separated list. If there are no such b values, enter NONE.) b + (1/b - 4) - 3

Learn how to simplify the expression b + (1/b - 4) - 3, combining terms and identifying when the expression is undefined. This algebra problem involves rational expressions and simplification techniques, suitable for students in Grades 8-10.

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