Answer
The rational expression B
Work Step by Step
Recall: A rational expression is in simplified form if the numerator and denominator of the expression have no common factors.
Factorize the denominator and numerator in each rational expression:
(A) $\frac{x^2-x-6}{x^2+3x+2}=\frac{(x-3)(x+2)}{(x+1)(x+2)}$
(B) $\frac{x^2+6x+8}{x^2+2x-3}=\frac{(x+2)(x+4)}{(x+3)(x-1)}$
(C) $\frac{x^2-6x+9}{x^2-2x-3}=\frac{(x-3)(x-3)}{(x-3)(x+1)}$
(D) $\frac{x^2+3x-4}{x^2+x-2}=\frac{(x+4)(x-1)}{(x+2)(x-1)}$
Note that the rational expressions (A), (C), and (D) have the common factors $(x+2)$, $(x-3)$, and $(x-1)$, respectively.
So, these expressions are not in simplified form.
Meanwhile, the rational expression (B) is in simplified form since the denominator and numerator have no common factors.
