The first step is to find the lowest common factor of each end of the fraction. The LCF of the numerator is 2 and the denominator is 4.
[tex] \frac{2x+6}{4x-12} = \frac{2(x+3)}{4(x-3)} [/tex]
From here, the only thing that can be simplified are the numbers outside the parenthesis, 2 and 4. 2 factors out, leaving a 1 on the top and a 2 on the bottom.
[tex] \frac{x+3}{2(x-3)} [/tex]
That's as far as it will simplify.
