Math Problem Statement

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

Solution

The expression in the image is:

xx+2+2x+2\frac{x}{x+2} + \frac{2}{x+2}

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

x+2x+2\frac{x + 2}{x+2}

Now, we can simplify by canceling out x+2x+2 in the numerator and the denominator (assuming x2x \neq -2 to avoid division by zero):

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

Final Answer: 11 (for x2x \neq -2).

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


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 x2x \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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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