Math Problem Statement
Solution
The expression you have provided is:
To simplify this, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of is .
Step-by-step process:
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Multiply the numerator and the denominator by the conjugate :
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Simplify the denominator using the difference of squares:
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Now the expression becomes:
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Simplify by dividing both the numerator and denominator by 2:
Thus, the simplified form of the expression is:
Would you like more details or have any questions?
Here are 5 related questions:
- How do you rationalize a denominator with multiple terms?
- What is the significance of the difference of squares in simplification?
- How can this technique be applied to more complex expressions?
- Can you explain why multiplying by the conjugate eliminates square roots in the denominator?
- How would the approach differ if both terms in the denominator were negative?
Tip: Always look for conjugates when simplifying radicals in the denominator.
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Math Problem Analysis
Mathematical Concepts
Algebra
Radical Expressions
Rationalization
Formulas
Difference of squares: \((a^2 - b^2) = (a - b)(a + b)\)
Theorems
Difference of squares theorem
Suitable Grade Level
Grades 9-11
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