Math Problem Statement
Solution
We are given the following expression:
Step 1: Factor each term
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First numerator: is a difference of squares, so:
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First denominator: is a perfect square trinomial, so:
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Second denominator: is also a perfect square trinomial, so:
Step 2: Rewrite the expression with factored terms
Step 3: Simplify by canceling common factors
- The factor appears once in the numerator and once in the denominator, so cancel one .
- Similarly, the factor appears in both, so cancel one .
After canceling, we are left with:
Final Answer:
The simplified expression is:
Would you like more details on any of these steps?
Here are 5 related questions:
- How do you factor a difference of squares?
- What are perfect square trinomials, and how do you factor them?
- Can you always simplify complex rational expressions by canceling factors?
- What happens if a variable in the denominator equals zero?
- How do you multiply two rational expressions?
Tip: Always check for common factors before multiplying rational expressions, as canceling early can save time.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Rational Expressions
Simplification
Formulas
Difference of squares: a^2 - b^2 = (a - b)(a + b)
Perfect square trinomials: a^2 + 2ab + b^2 = (a + b)^2, a^2 - 2ab + b^2 = (a - b)^2
Theorems
Factoring Theorem
Suitable Grade Level
Grades 9-11
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