Last one: 3x^2-15x+18 = (3x-6)(x-3)

x^2-x-6 = (x-3)(x+2)

Cancel out the (x-3) and you get (3x-6)/(x+2) = 3(x-2)/(x+2)

That’s as far as it goes.

(-x^2 + 8x + 48)

————————

(x^2 + x – 12)

then just deal with each part(top and bottom) one at a time. start with the top.

(-x^2 + 8x + 48)

factor out a -1, so your x^2 will be positive. it always helps if that is positive. so now you have

-1(x^2 – 8x – 48)

now you are going to split up what is in parenthesis into two different mini equations. you are looking for two numbers hat multiply to equal -48 and add to equal -8. your numbers are -12 and 4.

-1(x – 12)(x + 4)

now deal with the bottom

(x^2 + x – 12)

you are doing the same thing. two numbers that multiply to equal -12 and add to equal 1. -4 and 3.

(x – 4)(x + 3)

so now you have

-1(x – 12)(x + 4)

————————

(x – 4)(x + 3)

the (x + 4)’s cancel leaving you with

x + 12

———-

x + 3