Question

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

a. -6
b. 7
c. x+2
d. 2x-3

Answer 1

The answer is C. The numerator 7x+14 can be factored as 7(x+2). The denominator 2x^2+2x-6 can be factored as (x+2)(2x-3). The greatest common divisor of 7(x+2) and (x+2)(2x-3) is obviously x+2, which is contained in both of the two expressions.