(x^2-x-12)/(x-4)

2 min read Jun 17, 2024
(x^2-x-12)/(x-4)

Simplifying the Rational Expression (x^2-x-12)/(x-4)

This article explores the process of simplifying the rational expression (x^2-x-12)/(x-4).

Factoring the Numerator

The first step is to factor the numerator, x^2-x-12. We can achieve this by finding two numbers that multiply to -12 and add up to -1. These numbers are -4 and 3.

Therefore, we can rewrite the numerator as:

(x - 4)(x + 3)

Simplifying the Expression

Now we can rewrite the entire expression as:

(x - 4)(x + 3) / (x - 4)

Notice that both the numerator and denominator share a common factor, (x - 4). We can cancel these out, leaving us with:

(x + 3)

Restrictions

It's crucial to remember that simplifying the expression introduces a restriction. The original expression was undefined when x = 4, as this would lead to division by zero. Therefore, the simplified expression, x + 3, is valid for all values of x except x = 4.

Summary

In summary, simplifying the expression (x^2-x-12)/(x-4) results in x + 3, with the restriction that x ≠ 4.

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