Math Problem Statement
Simplify the expression \( \frac{3x}{x + 5} + \frac{4x}{x + 5} \).
Solution
To solve the expression:
Since both terms have the same denominator, , we can combine the fractions by adding the numerators directly:
So, the simplified form of the expression is:
Would you like a detailed explanation, or do you have any questions?
Here are five related questions for further exploration:
- What would happen if the denominators were different? How would you approach it?
- How can you simplify complex fractions with different variables?
- What if the expression had a subtraction sign instead of addition?
- How do you determine restrictions on for fractions to avoid division by zero?
- How do you handle cases where the numerator and denominator have common factors?
Tip: When adding or subtracting fractions, always check if you can combine them by using a common denominator.
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Math Problem Analysis
Mathematical Concepts
Algebra
Fraction Addition
Simplification
Formulas
\( \frac{a}{d} + \frac{b}{d} = \frac{a + b}{d} \) when denominators are the same
Theorems
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Suitable Grade Level
Grades 7-9