What is the value of $x$ if $x=\frac{2009^2-2009}{2009}$?
Factor 2009 out of the numerator: \[
\frac{2009^2-2009}{2009}=\frac{2009(2009-1)}{2009}=\boxed{2008}.
\]
2008
Level 2
Algebra
Problem: What is the value of $x$ if $x=\frac{2009^2-2009}{2009}$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the value of $x$, we start with the expression $x=\frac{2009^2-2009}{2009}$. First, we can simplify the expression in the numerator. The term $2009^2 - 2009$ can be factored as $2009(2009 - 1)$. This gives us:

$x = \frac{2009(2009 - 1)}{2009}$.

Next, we can cancel the $2009$ in the numerator and the denominator, assuming $2009 \neq 0$. This simplifies to:

$x = 2009 - 1$.

Now, performing the subtraction yields:

$x = 2008$.

Thus, the final answer is $2008$.<|END_OF_LATENT|> The final answer is $2008$.