Have I simplified the below correctly?
Problem 1:
3x^2 + 6x - 45 = x^2 + 2x - 15 = (x - 3) (x + 5)= answer of x-3 after cancellation
3x^2 + 21x +30   X^2 + 7x + 10   (x + 2) (x + 5)            x-2
Problem 2:
4a^2b^4 / 8ab^2 = 4A^2b = 4a^2b^4 * 1 = 4a^2b^4    = 4ab^2 = simplified to 1ab^2
3c^2      3c^2            8ab^2         24ab^2c^2    24c^2                 6c^2
Problem 3:
16x^2 - 1 / 4x + 1 = 16x^2 * y^3      =  simplified to 4xy
y^2         y^3      y^2     4x + 1
Thank you
You're NOT presenting your expressions in a way that they can be easily understood.
Anyway, based on the last one, I think you mean the following:
Problem # 1:   <====== This is what you have.
  <====== This is what you have.
               <====== This is what you should have.
Compare them and you'll see where you went wrong!!
Problem # 2:
  <====== This is what you should have.
Compare them and you'll see where you went wrong!!
Problem # 2:   <====== I THINK this is what you have.
  <====== I THINK this is what you have.
               <====== This is what you should have, if my HUNCH is right.
Compare them and you'll see where you went wrong!!
Problem # 3:
  <====== This is what you should have, if my HUNCH is right.
Compare them and you'll see where you went wrong!!
Problem # 3:  <====== I THINK this is what you have.
  <====== I THINK this is what you have.
              <==== This is what you should have, if my HUNCH is right.
Compare them and you'll see where you went wrong!!
  <==== This is what you should have, if my HUNCH is right.
Compare them and you'll see where you went wrong!!