(x^2-2x-48)/(x-8)

2 min read Jun 17, 2024

Simplifying the Expression (x^2 - 2x - 48) / (x - 8)

This expression represents a rational function, where the numerator and denominator are both polynomials. To simplify it, we can use the following steps:

1. Factor the Numerator

The numerator is a quadratic expression. We need to find two numbers that add up to -2 and multiply to -48. These numbers are -8 and 6. Therefore, we can factor the numerator as follows:

(x^2 - 2x - 48) = (x - 8)(x + 6)

2. Cancel Common Factors

Now, we have:

(x - 8)(x + 6) / (x - 8)

Notice that both the numerator and denominator share the factor (x - 8). We can cancel this common factor:

** (x + 6) / 1**

3. Simplify

The final simplified expression is:

x + 6

Important Note:

The original expression is undefined when x = 8 because the denominator becomes zero. This means the simplified expression is valid for all values of x except x = 8.

By factoring and simplifying the expression, we have transformed the original rational function into a simple linear expression. This simplified form can be easier to work with in various mathematical operations.