To simplify the given expression \(\dfrac{-2p + 8}{2p + 2}\), follow these steps:

1. Factor out the common factors in the numerator and the denominator.

The numerator \(-2p + 8\) can be factored as:
\[ -2(p - 4) \]

The denominator \(2p + 2\) can be factored as:
\[ 2(p + 1) \]

2. Substitute these factored forms back into the expression:
\[ \dfrac{-2(p - 4)}{2(p + 1)} \]

3. Cancel out the common factor of 2 in the numerator and the denominator:
\[ \dfrac{-2(p - 4)}{2(p + 1)} = \dfrac{-(p - 4)}{p + 1} \]

4. Distribute the negative sign in the numerator:
\[ \dfrac{-(p - 4)}{p + 1} = \dfrac{-p + 4}{p + 1} \]

Therefore, the simplified form of the given expression is:
\[ \dfrac{-p + 4}{p + 1} \]

Would you like more details or have any questions?

Here are 5 questions you might ask next:
1. How do you factor polynomials?
2. Can you show more examples of simplifying rational expressions?
3. What are the steps to solve a quadratic equation?
4. How do you add and subtract rational expressions?
5. Can you explain how to multiply and divide rational expressions?

**Tip:** Always look for common factors in the numerator and denominator when simplifying rational expressions.

Learn how to simplify the rational expression (-2p + 8) / (2p + 2) step-by-step. This problem involves algebraic manipulation of rational expressions, including factoring and cancelling out common factors. Suitable for high school students.

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