It looks like the image displays the following:
To simplify, you appear to be multiplying, top and bottom, by the LCM of the various denominators, being:
After multiplying, you get:
So I get the same products that you did. Then:
Each of the numerator and denominator can be factored, but nothing cancels. You can factor the numerator easily, as you have already displayed. You'll need to use
the Rational Roots Test to factor the denominator, and then the remaining quadratic is prime.
So the above is as "simplified" as you can get.