Okay so I tried solving it on my own, but I think I did the last step wrong. My answer was not correct. Can anyone show me a step by step answer on how to simplify this expression:

(3x + 1) / (x + 2) - (-5) / (x + 7)

2. $\frac{3x + 1}{x+2}-\frac{-5}{x+7}$
You will want to make the denominators equal, so you multiply the first fraction with $\frac{x+7}{x+7}$ and the second with $\frac{x+2}{x+2}$

$\frac{(3x+1)(x+7)}{(x+2)(x+7)}-\frac{-5(x+2)}{(x+2)(x+7)}$

$\frac{3x^2+x+21x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}$

$\frac{3x^2+22x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}$

$\frac{3x^2+27x+17}{(x+2)(x+7)}$
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?

3. Originally Posted by Pim
$\frac{3x + 1}{x+2}-\frac{-5}{x+7}$
You will want to make the denominators equal, so you multiply the first fraction with $\frac{x+7}{x+7}$ and the second with $\frac{x+2}{x+2}$

$\frac{(3x+1)(x+7)}{(x+2)(x+7)}-\frac{-5(x+2)}{(x+2)(x+7)}$

$\frac{3x^2+x+21x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}$

$\frac{3x^2+22x+7}{(x+2)(x+7)}-\frac{-5x-10}{(x+2)(x+7)}$

$\frac{3x^2+27x+17}{(x+2)(x+7)}$
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?
Yes thank you.