You can put this solution on YOUR website! a^2 + 3ab - 10b^2 factors out to be (a+5b) * (a-2b)
3a^2 - 7ab + 2b^2 factors out to be (3a-b) * (a-2b)
The (a-2b) in the numerator and denominator cancels out and you are left with:
(a+5b) / (3a-b)
I believe that's as simple as it can get.