Add the rational expressions: $$ \frac{5}{x}+\frac{1}{y} $$ define the domain $$ x
eq \square $$ $$ y
eq \square $$

Question

Add the rational expressions: $$ \frac{5}{x}+\frac{1}{y} $$ define the domain $$ x 
eq \square $$ $$ y 
eq \square $$

UpStudy AI · Accepted Answer

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
$$
x \neq 0 \quad \text{and} \quad y \neq 0.
$$
To add the rational expressions $$ \frac{5}{x} + \frac{1}{y} $$, find a common denominator, which is $$ xy $$. Rewrite each fraction with this denominator: $$ \frac{5}{x} = \frac{5y}{xy}, \quad \frac{1}{y} = \frac{x}{xy} $$ Add the fractions: $$ \frac{5y + x}{xy} $$ The domain is all real numbers except $$ x = 0 $$ and $$ y = 0 $$. So, the sum is $$ \frac{5y + x}{xy} $$ with $$ x \neq 0 $$ and $$ y \neq 0 $$.

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

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