%2F(x-4).jpeg "(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.