add parenthesis where needed in this equation. e^4x + e^−4x/e^4x − e^−4x

To correctly add parentheses and clarify the order of operations in the given expression, it should be written as:

\[
\frac{e^{4x} + e^{-4x}}{e^{4x} - e^{-4x}}
\]

This ensures that the entire numerator \( e^{4x} + e^{-4x} \) is treated as a single entity and the entire denominator \( e^{4x} - e^{-4x} \) is treated as another single entity.

Would you like a detailed explanation of how this expression is simplified or any other help?

Here are 5 related questions you might find useful:
1. How do you simplify the expression \(\frac{e^{4x} + e^{-4x}}{e^{4x} - e^{-4x}}\)?
2. What are the properties of exponents that apply to the expression \(\frac{e^{a} + e^{-a}}{e^{b} - e^{-b}}\)?
3. How do you solve equations involving exponents and logarithms?
4. What are the hyperbolic functions, and how are they related to expressions like the one given?
5. How does this expression change if \(e^x\) is replaced by a different base, like \(2^x\)?

**Tip:** When dealing with fractions in algebraic expressions, always use parentheses to clearly indicate the numerator and denominator to avoid ambiguity.

Learn how to correctly parenthesize and simplify the expression e^4x + e^-4x / e^4x - e^-4x. Understand the order of operations and how to handle fractional expressions involving exponential functions. Suitable for advanced high school students and those studying calculus or algebraic manipulation.

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