To simplify the expression:

\[
\frac{2b^2 + 2b - 4}{b - 2}
\]

1. **Factor the numerator**: 
   We start with \(2b^2 + 2b - 4\). Notice that each term has a factor of \(2\):
   \[
   2b^2 + 2b - 4 = 2(b^2 + b - 2)
   \]

   Now, factor \(b^2 + b - 2\):
   \[
   b^2 + b - 2 = (b + 2)(b - 1)
   \]

   So, the numerator becomes:
   \[
   2(b + 2)(b - 1)
   \]

2. **Rewrite the expression**:
   Substitute back into the original expression:
   \[
   \frac{2(b + 2)(b - 1)}{b - 2}
   \]

3. **Simplify**:
   There are no common factors between the numerator and the denominator, so the expression is already simplified as far as possible. 

The simplified form of the expression is:

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

Would you like more details on factoring or simplification? 

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Here are some related questions for deeper practice:

1. How do you simplify rational expressions with multiple terms in both the numerator and the denominator?
2. What techniques can you use to factor quadratic expressions efficiently?
3. What are the restrictions on the variable \(b\) in this expression?
4. How do you know when an expression is fully simplified?
5. Can you apply long division to simplify this expression differently?

**Tip:** Always look for common factors in an expression before starting the division or simplification process!

Simplify the rational expression (2b^2 + 2b - 4) / (b - 2) with a detailed step-by-step approach. This solution covers key algebraic concepts such as factoring and simplifying rational expressions, suitable for students in Grades 8-10.

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