# What is the least common denominator for \frac{2x}{x-4}+\frac{x}{4-x}?

$x - 4$.
When you multiply the second fraction with $- 1$, you get
$\frac{2 x}{x - 4} + \frac{- x}{-} \left(4 - x\right) = \frac{2 x}{x - 4} + \frac{- x}{x - 4} = \frac{x}{x - 4}$