Math Problem Statement
Solution
The image shows a complex rational expression involving division of two fractions. The given expression is:
Steps to simplify:
- Division of Fractions Rule: To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. So, we rewrite the expression as:
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Factor the Numerators and Denominators:
- Factor (difference of squares):
- Factor (perfect square trinomial):
- Factor : Find two numbers whose product is and sum is . The factorization is:
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Multiply the Factored Expressions:
Now we have:
Next, check if the numerator can be factored further. In this case, it cannot be factored nicely.
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Simplify the Expression:
After multiplying, the expression becomes:
This is the simplified form of the original expression.
Would you like further clarification on any step or details?
Related Questions:
- How do you find the reciprocal of a rational expression?
- What are the steps to factor quadratic expressions?
- Why do we multiply by the reciprocal when dividing fractions?
- Can you further simplify the expression if or ?
- How can you solve rational equations?
Tip: Always check for common factors to cancel out when simplifying rational expressions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Expressions
Factoring
Multiplication of Fractions
Formulas
(a^2 - b^2) = (a - b)(a + b)
Factoring Quadratic Trinomials
Theorems
Division of Fractions Rule
Suitable Grade Level
Grades 10-12
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