Add the rational expressions: \( \frac{5}{x}+\frac{1}{y} \) define the domain \( x \neq \square \) \( y \neq \square \)

To add the rational expressions, we first find a common denominator. 1. The given expressions are: \[ \frac{5}{x} + \frac{1}{y} \] 2. The common denominator for \(x\) and \(y\) is \(xy\). 3. Rewrite each fraction with the denominator \(xy\): \[ \frac{5}{x} = \frac{5y}{xy}, \quad \frac{1}{y} = \frac{x}{xy} \] 4. Now add the fractions: \[ \frac{5y}{xy} + \frac{x}{xy} = \frac{5y+x}{xy} \] 5. Define the domain. Since denominators \(x\) and \(y\) cannot be zero, we have: \[ x \neq 0, \quad y \neq 0 \] Thus, the final result is: \[ \frac{5}{x} + \frac{1}{y} = \frac{5y+x}{xy} \] with the domain \[ x \neq 0 \quad \text{and} \quad y \neq 0. \]