Trinomials in Algebra 2

3x^2+7x-6 divided by 3x^2-27

x^2-9 divided by 2x^2-5x-3

3x^2+7x-6 divided by 3x^2-27
= (3x^2+7x-6) / ( 3x^2-27)
= ( 3x -2)(x +3) / 3 ( x^2 -3^2)
= (3x -2) ( x+3) / 3 ( x -3)(x+3)
= (3x -2) / 3(x-3)

x^2-9 divided by 2x^2-5x-3
= (x^2-9) / ( 2x^2-5x-3)
= (x-3)(x+3) / ( 2x +1)(x -3)
= (x+3) / (2x+1)

First, factor completely.
Then divide out any factors that appear in both numerator and denominator remembering that the denominator can't be zero, so for example if you have a rational fxn where you have x+3 in both, x can never be -3