(x+3)/(x-3) Simplify

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (x+3)/(x-3)

The expression (x+3)/(x-3) is a rational expression, meaning it is a fraction where the numerator and denominator are polynomials. While it can be simplified to some extent, it's important to note that there are no further simplifications possible beyond factoring out common factors.

Here's why:

1. Factoring: We can factor both the numerator and denominator:

   • Numerator: (x+3) is already in its simplest form.
   • Denominator: (x-3) is already in its simplest form.

2. Cancellation: We can cancel out any common factors between the numerator and denominator. However, in this case, there are no common factors.

Therefore, the expression (x+3)/(x-3) is already in its simplest form.

Important Notes:

• Undefined Values: The expression is undefined when the denominator is zero. This occurs when x = 3.
• Restrictions: When working with rational expressions, it's crucial to identify any restrictions on the variable. In this case, x cannot equal 3.

In summary, while the expression (x+3)/(x-3) cannot be simplified further, it's important to recognize its restrictions and the values for which it's undefined.