Math Problem Statement

\dfrac{-2p + 8}{2p + 2}

Solution

To simplify the given expression 2p+82p+2\dfrac{-2p + 8}{2p + 2}, follow these steps:

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

The numerator 2p+8-2p + 8 can be factored as: 2(p4)-2(p - 4)

The denominator 2p+22p + 2 can be factored as: 2(p+1)2(p + 1)

  1. Substitute these factored forms back into the expression: 2(p4)2(p+1)\dfrac{-2(p - 4)}{2(p + 1)}

  2. Cancel out the common factor of 2 in the numerator and the denominator: 2(p4)2(p+1)=(p4)p+1\dfrac{-2(p - 4)}{2(p + 1)} = \dfrac{-(p - 4)}{p + 1}

  3. Distribute the negative sign in the numerator: (p4)p+1=p+4p+1\dfrac{-(p - 4)}{p + 1} = \dfrac{-p + 4}{p + 1}

Therefore, the simplified form of the given expression is: p+4p+1\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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Expressions

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12