solving equations

I have an extra credit question that I am trying to solve:

If f(x)= 1/x+2 and g(x)= 3x, solve for (f-g)x

So far, I am thinking f(x)=1/x+2 x g(x)= 3/x+2.
So, 1/x+2-3x squared+6x/x+2
and, then, -3 squared-6x-1/x+2.

Is that right?

You must first fix your notation. Use parentheses to clarify intent.

1/x+2 what do you mean (1/x)+2 or 1/(x+2). They're not the same.

Assuming the latter, haven't we: \(\displaystyle (f-g)(x) = \frac{1}{x+2} - 3x = \frac{1 - 3x(x+2)}{x+2}\)

Rather than go on, with my switched around example, I'll let you tell me what it is that you mean.