Math Problem Statement
Simplify the expression: (2p / (p^2 - q^2)) ÷ (4q / (p + q)).
Solution
The expression in the image appears to be:
Let's simplify this step by step:
Step 1: Factorize the denominator
The denominator is a difference of squares, which can be written as:
So the expression becomes:
Step 2: Simplify the multiplication
Now multiply the numerators and denominators:
Cancel out the common factor (assuming ):
Step 3: Simplify further
Combine and in the denominator:
Final Simplified Expression:
Would you like me to provide additional details or further explain any steps?
Related Questions:
- How do you factorize other types of polynomials like ?
- Why is the difference of squares formula important in algebra?
- What conditions must hold true for terms to be canceled in fractions?
- How do you handle cases where or ?
- What are some practical applications of simplifying algebraic fractions?
Tip:
Always check for factors that can be canceled, but ensure that the terms you're canceling are not equal to zero!
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Simplifying Rational Expressions
Formulas
Difference of squares: a^2 - b^2 = (a - b)(a + b)
Theorems
Properties of Rational Expressions
Multiplication and Division of Fractions
Suitable Grade Level
Grades 8-10