Simplify .

Kick things off by factoring the numerator and denominator.

Hey, check it out: those x + 3 terms cancel each other out in a puff of purple smoke.

That leaves us with just a 4 up top and a 5 down low.

Simplify .

Factor the numerator and denominator, then cancel out all the stuff you possibly can. Seriously, just really hack away at this thing.

Nice. Now that we kicked 2 and y + 9 to the curb, we're left with our simplified form:

Simplify .

Let's tackle the numerator and denominator separately for a sec. First off, we can pull a 3 out of 3c² – 27:

3c² – 27 = 3(c² – 9)

Then factor the stuff in parentheses as a difference of squares:

3(c² – 9) = 3(c – 3)(c + 3)

Beautiful. The denominator, c² + c – 6, factors nicely into (c – 2)(c + 3). Now we can rewrite our entire fraction.

Cancel like factors.

Which give us: