Originally Posted by
Pim $\displaystyle \frac{3x + 1}{x+2}-\frac{-5}{x+7}$
You will want to make the denominators equal, so you multiply the first fraction with $\displaystyle \frac{x+7}{x+7}$ and the second with $\displaystyle \frac{x+2}{x+2}$
$\displaystyle \frac{(3x+1)(x+7)}{(x+2)(x+7)}-\frac{-5(x+2)}{(x+2)(x+7)}$
$\displaystyle \frac{3x^2+x+21x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}$
$\displaystyle \frac{3x^2+22x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}$
$\displaystyle \frac{3x^2+27x+17}{(x+2)(x+7)}$
Note that you need to do - (-5x-10) which comes down to +5x+10
Some people prefer to multiply out the denominator, but I personally don't.
Does this make it clear?