My work on simplifying this function: g(x)=(-3x^2-13x-13)

g(x)=-3x^2-13x-13 (13x-13=x)
g(x)=-3x^2-x

Can someone help with the simplifying the function if I have got it wrong and also can someone tell me of it's equivalent to this function:f(x)=-3(x+2)^2-(x+1)

Also I have another function that I have to simplify:g(x)=(x-2)/(3x+1)
My work:
As far as I'm aware there is no way to simplify the above stated function but if someone could help me with it, your help would greatly appreciated and also if it's equivalent to this function:f(x)=(x^2-x-2)/(3x^2-+4x+1)

I can not simplify it but

f(x) = -3(x^2+4x+4) -x-1
= -3 x^3 -12 x -12 - x - 1
= -3x^2 - 13 x -13 sure enough

f(x) = [(x-2)(x+1)] / [ (3x+1)(x+1) ]
= (x-2)/(3x+1) we win again

Damon so are the simplified versions of the functions equivalent to their respective functions?

To simplify the function g(x) = -3x^2 - 13x - 13, let's first check if your simplification is correct.

g(x) = -3x^2 - 13x - 13 (13x - 13 = x)
g(x) = -3x^2 - x

Your simplification is incorrect. To simplify the function, you need to rewrite it in a more simplified form, if possible.

Now, let's see if the given function g(x) = -3x^2 - 13x - 13 is equivalent to f(x) = -3(x + 2)^2 - (x + 1).

Expanding f(x) = -3(x + 2)^2 - (x + 1):
f(x) = -3(x^2 + 4x + 4) - (x + 1)
f(x) = -3x^2 - 12x - 12 - x - 1
f(x) = -3x^2 - 13x - 13

Therefore, g(x) = f(x). The two functions are equivalent.

Moving on to the second function g(x) = (x - 2)/(3x + 1).

Your statement that there is no way to simplify the function g(x) is incorrect. We can indeed simplify the function and write it in a more simplified form.

To simplify g(x) = (x - 2)/(3x + 1), we can use polynomial division or factorization. Let's use factorization method.

g(x) = (x - 2)/(3x + 1)

For the numerator (x - 2), let's rewrite it as the difference of two squares:
x - 2 = (x - 1) - 1

Now, let's rewrite the function g(x) using this simplification:
g(x) = ((x - 1) - 1)/(3x + 1)

We can further simplify it as:
g(x) = (x - 1)/(3x + 1) - 1/(3x + 1)

Therefore, the simplified form of g(x) = (x - 2)/(3x + 1) is g(x) = (x - 1)/(3x + 1) - 1/(3x + 1).

As for the equivalence with the given function f(x) = (x^2 - x - 2)/(3x^2 + 4x + 1), they are not equivalent. The function g(x) cannot be simplified to match f(x).