Answer
0
Work Step by Step
Before we add, we want a common denominator on both terms. The LCM of these two terms (least common multiple) is $x-5$, which would involve keeping the first term untouched and multiplying the second term by $-1/-1$.
$\frac{x}{x-5} + \frac{x}{5-x} = \frac{x}{x-5} + \frac{x}{5-x}\cdot\frac{-1}{-1} = \frac{x}{x-5}-\frac{x}{x-5} = 0$
