How would you simplify using factors?

Question

3a^3 - 27a over 2a^2 + 13a -7 divided by 9a^2 over 4a^2 - 1

is this even possible?

i need step by step

the farthest i got was (a^2-9) over (2a^1)(a + 7) times 4a^2-1 over 3a

Answer 1

After flipping the second one you have these factors:

top........3a(a+3)(a-3) (2a + 1)(2a - 1)

bottom..(2a - 1)(a + 7)(9a^2)

So the 3a cancels the 9a^2 leaving 3a on bottom

the (2a - 1) cancels leaving

top.....(a+3)(a-3)(2a + 1)

bottom 3a(a+7)

Answer 2

3a(a^2-9)/ (2a-1  )(a  +7) divided by  9a^2/ (2a+1)(2a-1)

3a(a+3)(a-3))/ (2a-1  )(a  +7) * (2a+1)(2a-1)/9a^2

2a-1 simplifies

3a(a+3)(a-3))/ (a  +7) * (2a+1)/3a*3a

the 3a simplifies

(a+3)(a-3))/ (a  +7) * (2a+1)/3a

= (a+3)(a-3)(2a+1)/ 3a(a+7)