Expressing an algebraic function as a single expression I have the following question in my text book:
Express as a single fraction
$$ \frac{3}{x-4} - \frac{2}{(x-4)^2} $$
The answer the book gives is this:
$$ \frac{3x-14}{(x-4)^2} $$
I understand how they get to this through these steps:
$$ \frac{3(x-4)-2}{(x-4)^2} = \frac{3x-12-2}{(x-4)^2} $$
My question is why can you not cancel the $$ (x-4) $$ instead like this:
$$ \frac{3(x-4)-2}{(x-4)^2} = \frac{3-2}{(x-4)} = \frac{1}{(x-4)} $$

in your last line you can't cancel the $(x-4)$! You have 
$$
  \frac{3(x-4) - 2}{(x-4)^2} = \frac{3 - \frac 2{x-4}}{x-4} \ne \frac{1}{x-4}.
$$
Just as in, say $\frac{3+4}9$, you can't cancel the $3$ to obtain $\frac{1+4}{3} = \frac 53$.
