Question

What is the greatest common factor of the numerator and denominator

Answer 1

In the numerator, we can pull a 7 out of the expression 7x + 14 to get the product 7(x + 2). In the denominator, we can factor the expression 2x² + x - 6 like this:

$2x^2+x-6=2x^2+4x-3x-6\\=2x(x+2)-3(x+2)\\=(x+2)(2x-3)$

Our fraction can now be written as

$\dfrac{7(x+2)}{(x+2)(2x-3)}$

the only factor the numerator and denominator share in this case is x + 2.