Answer:
9) (a² + 9)/3 10) (2a - 1)/a 11) (3x + 1)/(2x + 3) 12) (x- 2y) / (x+2y)
Explanation:
9) Had to simplify the numerator and denominator using difference of squares. a^4 - 81 is a difference of two perfect squares. This breaks down to (a² + 9)(a² - 9). The denominator had a GCF of 3, which became 3(a² - 9). Rather than breaking both of the (a² - 9)'s down to (a-3)(a+3), you can cancel them out. That leaves you the answer.
10) The numerator factors to (2a - 1)(a + 6). The method behind factoring is taught 100 different ways. I'd suggest youtubing a video of "How to factor a trinomial". The denominator has a GCF of a. Making that a(a+6). The two (a+6)'s cancel and you're left with the answer.
11) The numerator factors to (2x + 3)(3x + 1), the denominator factors to (2x+3)(2x + 3). So the (2x+3) cancels out and you're left with the answer.
12) The numerator simplifies to (x - 2y)(x - 2y). The denominator is a difference of squares (x + 2y)(x - 2y). The (x - 2y)'s cancel out. Left with the answer!
Enjoy.