I don't know if this is a good way to do this, but...
First, you can factor the numerator, which is 15x2−8x−7, to (x−1)(15x+7).
We can do the same thing with the denominator x2−2x+1, to (x−1)2.
Now, we have (x−1)(15x+7)(x−1)2. And, we can cancel x−1, since that is our common factor. Thus, we are left with 15x+7x−1.
If you need more explanation on the factoring, just tell me. Also, I think synthetic division works.

