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:
[tex] 2x^2+x-6=2x^2+4x-3x-6\\=2x(x+2)-3(x+2)\\=(x+2)(2x-3) [/tex]
Our fraction can now be written as
[tex] \dfrac{7(x+2)}{(x+2)(2x-3)} [/tex]
the only factor the numerator and denominator share in this case is x + 2.
