Write this expression in simplest form. 4r^2-25s^2 over 2r^2 + 3rs - 20s^2?

Question

Algebra is a tough subject for me can any one help

Answer 1

4r^2-25s^2
-----------------------
2r^2 + 3rs - 20s^2

1.) Factor out the top half.
4r^2 - 25s^2 =
Factoring squares:
a^2 * x^2 - b^2 *y^2 = (ax + by) (ax - by)
so:
4r^2 - 25s^2 = (2r + 5s) (2r - 5s)

2.) Factor out the bottom half:
2r^2 + 3rs - 20s^2

Note: The one part I don't remember, is the intermediate steps to reduce this polynomial here...but the reduction is:
(2r - 5s) (r + 4s)

3.) Combine them:
(2r + 5s) (2r - 5s)
---------------------------
(2r - 5s) (r + 4s)

The 2r - 5s part cancels:
(2r + 5s)/(r + 4s) (solution!)

Answer 2

I'm pretty sure it's

-21 over -18 + 3rs

Good luck, hope it's right

Answer 3

2 points. Don't get much more simple then that