Math Problem Statement

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

Solution

The expression provided is:

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

Since both terms have a common denominator of x+5x + 5, we can combine them by adding the numerators:

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

So, the simplified expression is:

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

Would you like a further breakdown or have any questions?

Here are 5 related questions to expand on this:

  1. How would you simplify an expression with different denominators?
  2. What happens if you factor the numerator and denominator further?
  3. How does the solution change if one term had a different denominator?
  4. How do you simplify expressions when variables are in both numerator and denominator?
  5. What are some common methods for simplifying fractions?

Tip: When adding fractions with the same denominator, combine the numerators and keep the denominator as it is.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Fractions
Addition of Fractions with Common Denominator

Formulas

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

Theorems

Addition of Fractions with Common Denominator

Suitable Grade Level

Grades 7-8