I can get this question right except for the last part.

$\displaystyle \frac{1}{2x-2}+\frac{3}{4x-8}$

The non-reduced answer i end up getting is:

$\displaystyle \frac{10x-14}{12(x-2)(x-1)}$

My question is when you are simplfying this question why is it that you divide the numerator by 2 and the denominator by 3?? Aren't the numerator and the denominator supposed to be divided by the same numbers

My answer:

$\displaystyle \frac{5x-7}{6(x-2)(x-1)}$

Book answer:

$\displaystyle \frac{5x-7}{4(x-2)(x-1)}$