What is the difference of r+2/r+4 and 3/r+1?

I assume you mean:

(r+2) / (r+4) - 3 / (r+1) we need a common denominator of (r+1) (r+4)

[ (r+2) (r+1) - 3 (r+4) ] / (r^2+5r+4)

(r^2+3r+2-3r-12) / (r^2+5r+4)

(r^2-10) / (r^2+5r+4)

now you could factor out the answer if you wanted to ...

((r+√10) (r-√10)) / ((r+1) (r+4))