Math Problem Statement
Solution
Let's simplify the given polynomial expression step by step:
Step 1: Factorize where possible
-
The term is a difference of squares:
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The denominator can be factored as:
Now, rewriting the expression with factored terms:
Step 2: Cancel common factors
- The in the numerator and denominator cancel out.
- The in the numerator and denominator also cancel out.
After cancellation, we are left with:
Step 3: Simplify the fraction
Step 4: Choose the correct answer
The correct answer is:
which corresponds to the first option.
Would you like a further breakdown of any step? Here are five related questions for further practice:
- How do you factorize quadratic expressions like ?
- Why does canceling common factors work in fraction multiplication?
- What is the general formula for the difference of squares?
- How do you simplify algebraic fractions with multiple terms?
- How would this process change if the expression involved division instead of multiplication?
Tip: Always factorize expressions before multiplying or dividing to simplify the process.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Simplification
Factoring
Formulas
Difference of Squares: a^2 - b^2 = (a - b)(a + b)
Fraction Multiplication: (A/B) * (C/D) = (A*C) / (B*D)
Theorems
Factorization Theorem
Basic Fraction Reduction
Suitable Grade Level
Grades 8-10
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