Final answer:
The greatest common factor (GCF) of the numerator and denominator in the rational function 7x+14 / 2x^2+x-6 is 7(x + 2).
Step-by-step explanation:
The greatest common factor (GCF) of the numerator and denominator in the rational function 7x+14 / 2x^2+x-6 can be found by factoring the expressions in the numerator and denominator and identifying the common factors. First, let's factor the numerator:
7x + 14 = 7(x + 2)
Now, let's factor the denominator:
2x^2 + x - 6 = (x + 3)(2x - 2)
The common factors between the numerator and denominator are 7 and (x + 2).
Therefore, the greatest common factor (GCF) is 7(x + 2).