Final answer:
The rational expression (x² + 5x + 6) / (x² - x - 6) simplifies to B. x + 3 / x - 3 after factoring and canceling out common factors.
Step-by-step explanation:
The given problem requires simplifying a rational expression, which is a part of algebra in mathematics. To find which of the given options is equal to the expression (x² + 5x + 6) / (x² - x - 6), we need to factor both the numerator and denominator. Factorization of a quadratic expression is done by finding two numbers that multiply to give the product of the coefficient of x² and the constant term, and add to give the coefficient of x.
Let's factor both numerator and denominator:
- Numerator: x² + 5x + 6 = (x + 2)(x + 3)
- Denominator: x² - x - 6 = (x - 3)(x + 2)
After factoring, the expression simplifies to:
(x + 2)(x + 3) / (x - 3)(x + 2)
We observe that (x + 2) is in both the numerator and denominator, so they cancel each other out. The simplified form of the expression will be:
(x + 3) / (x - 3)
Therefore, the correct answer is B. x + 3 / x - 3.