Question

What is the greatest common factor (GCF) of the numerator and denominator in the rational function 7x+14 / 2x^2+x-6?

A) 1
B) 2x+7
C) 2
D) 3x-2

Answer 1

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).