Math Problem Statement
Simplify the expression \( \frac{x}{x+2} + \frac{2}{x+2} \).
Solution
The expression in the image is:
Since both terms have the same denominator , we can combine them directly:
Now, we can simplify by canceling out in the numerator and the denominator (assuming to avoid division by zero):
Final Answer: (for ).
Would you like additional details, or do you have any questions?
Here are some related questions to deepen your understanding:
- How would this change if the denominators were different?
- What is the significance of the restriction ?
- How do you handle cases where the denominator might be zero?
- Can you perform similar simplifications for other expressions with common denominators?
- 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.
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Math Problem Analysis
Mathematical Concepts
Algebra
Fraction Simplification
Common Denominators
Formulas
\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}
Theorems
Properties of Rational Expressions
Suitable Grade Level
Grades 7-9