https://file.aiquickdraw.com/mathbot/file/17303197662742un1tvgc.jpg

The expression in the image is:

\[
\frac{x}{x+2} + \frac{2}{x+2}
\]

Since both terms have the same denominator \( x + 2 \), we can combine them directly:

\[
\frac{x + 2}{x+2}
\]

Now, we can simplify by canceling out \( x+2 \) in the numerator and the denominator (assuming \( x \neq -2 \) to avoid division by zero):

\[
\frac{x + 2}{x+2} = 1
\]

**Final Answer:** \( 1 \) (for \( x \neq -2 \)).

Would you like additional details, or do you have any questions?

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Here are some related questions to deepen your understanding:

1. How would this change if the denominators were different?
2. What is the significance of the restriction \( x \neq -2 \)?
3. How do you handle cases where the denominator might be zero?
4. Can you perform similar simplifications for other expressions with common denominators?
5. How would this simplification apply if there were three or more terms with the same denominator?

**Tip:** Always check for any values that could make the denominator zero when simplifying fractions.

Simplify the expression \( \frac{x}{x+2} + \frac{2}{x+2} \).

Learn how to simplify the algebraic expression \( \frac{x}{x+2} + \frac{2}{x+2} \) by combining terms with common denominators. This problem introduces key concepts in fraction simplification and rational expressions, suitable for Grades 7-9.

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