(2n-1) /(2n+1) Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2n-1)/(2n+1)

The expression (2n-1)/(2n+1) is a rational expression, meaning it is a fraction where the numerator and denominator are polynomials. In this case, we have a simple binomial in both the numerator and denominator. It's important to note that this expression cannot be simplified further.

Here's why:

• No common factors: The numerator and denominator share no common factors that can be canceled out. We can't factor out a 2, an n, or anything else that appears in both expressions.

Important Considerations

It's tempting to try to simplify by canceling the '2n' terms. However, this is incorrect. Remember that in a fraction, you can only cancel factors that are multiplied throughout the entire numerator and denominator. In this case, the '2n' is part of a sum or difference, not a simple multiplication.

Example:

Imagine we have the expression (2n - 1) / (2n + 1) and we want to evaluate it for n = 3.

• (2 * 3 - 1) / (2 * 3 + 1)
• (6 - 1) / (6 + 1)
• 5 / 7

This demonstrates that the expression (2n - 1)/(2n + 1) can be evaluated for different values of 'n', resulting in different fractional values. It cannot be simplified to a single number or a simpler expression.