To write \(\frac{-4}{x} + \frac{7}{y}\) as a single fraction, follow these steps:

1. Find a common denominator, which in this case is \(xy\).
   
2. Rewrite each fraction with the common denominator:
   \[
   \frac{-4}{x} = \frac{-4y}{xy}, \quad \frac{7}{y} = \frac{7x}{xy}
   \]

3. Now, combine the fractions:
   \[
   \frac{-4y}{xy} + \frac{7x}{xy} = \frac{-4y + 7x}{xy}
   \]

Thus, \(\frac{-4}{x} + \frac{7}{y}\) as a single fraction is:
\[
\frac{7x - 4y}{xy}
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would you simplify \(\frac{5}{x} - \frac{2}{y}\)?
2. What is the result of combining \(\frac{a}{b} + \frac{c}{d}\) into a single fraction?
3. Can you express \(\frac{3}{x} - \frac{9}{y}\) as a single fraction?
4. How do you add fractions with different denominators in general?
5. How does this process apply to fractions involving more complex expressions?

**Tip:** Always ensure the denominators are the same before combining fractions!

Learn how to combine -4/x + 7/y into a single fraction with step-by-step guidance. This problem covers key algebra concepts like rational expressions and finding a common denominator, suitable for Grades 8-10.

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