%2F(x%2B5)-simplify.jpeg "(x-5)/(x+5) Simplify")
Simplifying the Expression (x-5)/(x+5)
The expression (x-5)/(x+5) is a simple rational expression, meaning it's a fraction where both the numerator and denominator are polynomials. While it cannot be simplified further, there are a few key points to consider:
Understanding the Expression
- It's a fraction: The expression is a fraction, with (x-5) as the numerator and (x+5) as the denominator.
- Not a cancellation: You cannot simply cancel out the 'x' terms in the numerator and denominator. This is a common mistake. Remember, in fractions, we can only cancel out factors that are common to both the numerator and denominator.
What does "simplify" mean?
"Simplifying" a fraction usually means:
- Factoring: Try to factor both the numerator and denominator to see if there are any common factors that can be canceled out.
- Reducing to lowest terms: Once you've factored, cancel out any common factors to get the simplest form.
Why can't we simplify (x-5)/(x+5) further?
In this case, both the numerator (x-5) and the denominator (x+5) are already in their simplest factored forms. There are no common factors to cancel out. Therefore, the expression (x-5)/(x+5) is considered already simplified.
Important Note:
It's crucial to remember that this expression is not defined when x = -5 because it would lead to division by zero.
Therefore, the simplified form of (x-5)/(x+5) is itself, with the restriction that x ≠ -5.