Math Problem Statement
Solution
To solve and simplify the given problem:
Step 1: Common Denominator
Both fractions already have the same denominator: . So we can combine the numerators directly:
Step 2: Combine the Numerators
Simplify the numerator :
- Combine like terms:
Thus, the numerator simplifies to .
Step 3: Simplify the Expression
The simplified fraction is:
Now, factor the denominator . This quadratic can be factored as:
Step 4: Cancel Common Factors
The numerator and one factor in the denominator cancel out (as long as , to avoid division by zero):
Final Simplified Answer:
Would you like a detailed explanation of any specific step? Let me know!
Related Questions:
- How do you factor a quadratic expression like ?
- What are the restrictions on the variable when simplifying rational expressions?
- How do you combine fractions with a common denominator?
- What happens when terms in the numerator and denominator cancel?
- How can you check your final simplified expression for correctness?
Tip:
Always check for restrictions (values that make the denominator zero) when simplifying rational expressions!
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Math Problem Analysis
Mathematical Concepts
Rational Expressions
Factoring Polynomials
Simplifying Fractions
Formulas
Combining fractions: a/b + c/b = (a + c)/b
Factoring quadratic equations: z^2 - 7z + 12 = (z - 3)(z - 4)
Theorems
Cancellation Property of Rational Expressions
Suitable Grade Level
Grades 9-11