-%2F(n-1)-simplify.jpeg "(n+1) /(n-1) Simplify")
Simplifying the Expression (n+1)/(n-1)
The expression (n+1)/(n-1) represents a fraction where the numerator is (n+1) and the denominator is (n-1). While this expression is already in its simplest form in terms of factoring, there are no further simplifications possible. However, we can analyze the expression and understand its behavior.
Understanding the Expression
- Undefined Values: The expression is undefined when the denominator is zero. This occurs when n = 1.
- Asymptotes: As n approaches 1, the denominator approaches zero, causing the fraction to grow infinitely large. This means there is a vertical asymptote at n=1.
- Horizontal Asymptote: As n approaches positive or negative infinity, the expression approaches 1. This is because the numerator and denominator have the same degree (both are linear), and their leading coefficients are equal. Therefore, there is a horizontal asymptote at y = 1.
Limitations of Simplification
It's important to note that we cannot simplify (n+1)/(n-1) further by canceling out the 'n' terms. This is because:
- n is a variable: The 'n' terms are not constants; they represent any possible value.
- Incorrect Cancellation: Cancelling 'n' would be equivalent to dividing the numerator and denominator by 'n', which is not a valid operation unless 'n' is a constant.
Conclusion
The expression (n+1)/(n-1) is already simplified. However, understanding its behavior with regards to undefined values and asymptotes can provide valuable insights into its properties.