Math Problem Statement
Solution
We need to simplify the given rational expression:
Step 1: Factor the numerator
The numerator is . We will factor this quadratic expression. We need to find two numbers that multiply to and add to . These numbers are and . Thus, we can factor the numerator as:
Step 2: Factor the denominator
The denominator is . We will factor this cubic expression by grouping.
Factor out from the first group and from the second group:
Now, factor as a difference of squares:
Thus, the denominator becomes:
Step 3: Simplify the expression
Now we have the following expression:
We can cancel out the common factors and :
Final Answer:
The simplest form of the expression is:
Thus, the correct answer is c.
Would you like further clarification or details?
Here are 5 related questions:
- How do you factor quadratic expressions in general?
- What is the method of factoring by grouping?
- How do you simplify rational expressions?
- Can you always cancel terms in the numerator and denominator?
- What are difference of squares, and how are they factored?
Tip: When simplifying rational expressions, always check for common factors in both the numerator and the denominator.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring Polynomials
Rational Expressions
Formulas
Difference of Squares: \(a^2 - b^2 = (a - b)(a + b)\)
Theorems
Difference of Squares
Suitable Grade Level
Grades 9-12
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