Math Problem Statement
Simplify the expression (e^(2x) - e^x + 1) / e^x
Solution
Let's simplify the given expression:
Step-by-Step Solution:
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Break down the terms in the numerator: The expression can be seen as a fraction, where we can split the terms:
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Simplify each term:
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Combine the results:
Thus, the simplified form of the original expression is:
Would you like a more detailed explanation or have any questions?
Here are some related questions to deepen your understanding:
- How do you simplify expressions involving exponential functions in general?
- What are the properties of exponents that allow us to simplify ?
- Can the simplified expression be factored further?
- What are some common mistakes to avoid when simplifying expressions like this?
- How would you differentiate or integrate the simplified expression?
Tip: Remember, when dividing exponential functions with the same base, you subtract the exponents!
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Algebraic Manipulation
Formulas
e^(a + b) = e^a * e^b
e^a / e^b = e^(a - b)
Theorems
Properties of Exponents
Suitable Grade Level
Grades 10-12