Math Problem Statement

Simplify the expression \( \frac{3x}{x + 5} + \frac{4x}{x + 5} \).

Solution

To solve the expression:

3xx+5+4xx+5\frac{3x}{x + 5} + \frac{4x}{x + 5}

Since both terms have the same denominator, x+5x + 5, we can combine the fractions by adding the numerators directly:

3x+4xx+5=7xx+5\frac{3x + 4x}{x + 5} = \frac{7x}{x + 5}

So, the simplified form of the expression is:

7xx+5\frac{7x}{x + 5}

Would you like a detailed explanation, or do you have any questions?


Here are five related questions for further exploration:

  1. What would happen if the denominators were different? How would you approach it?
  2. How can you simplify complex fractions with different variables?
  3. What if the expression had a subtraction sign instead of addition?
  4. How do you determine restrictions on xx for fractions to avoid division by zero?
  5. 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