Math Problem Statement
Solution
We are tasked with simplifying the following rational expression:
Step-by-step Solution:
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Factorize each part of the expression:
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Factorize the numerator :
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Factorize the denominator :
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Factorize the denominator :
Substituting these factorizations, the expression becomes:
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Simplify by canceling common factors:
- appears in both the numerator and denominator, so cancel .
- appears in both the numerator and denominator, so cancel .
- in the numerator of the second fraction cancels with the in the denominator of the first fraction.
After cancellation, we are left with:
Final Answer:
Note:
The expression is valid for , as these values would make the original denominators equal to zero.
Do you want further clarification or details on any of these steps?
Related Questions:
- How do you factor trinomials like ?
- Why is it important to find restrictions on in rational expressions?
- What happens if a factor is not canceled correctly in such problems?
- How can you confirm your factorizations are correct?
- How do you approach similar problems involving division instead of multiplication?
Tip:
Always check for factors common to both the numerator and denominator before simplifying—it helps avoid mistakes!
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Simplification of Rational Expressions
Formulas
Factoring trinomials: ax^2 + bx + c = (px + q)(rx + s)
Simplifying rational expressions: Canceling common factors in numerators and denominators
Theorems
Zero Product Property
Properties of Rational Expressions
Suitable Grade Level
Grades 8-10
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