simplify fraction x+3 over 5 plus x-2 over 3

To simplify the expression:

\[
\frac{x+3}{5} + \frac{x-2}{3}
\]

1. Find the least common denominator (LCD) of 5 and 3, which is 15.

2. Rewrite each fraction with 15 as the denominator:
   \[
   \frac{x+3}{5} = \frac{3(x+3)}{15} = \frac{3x + 9}{15}
   \]
   \[
   \frac{x-2}{3} = \frac{5(x-2)}{15} = \frac{5x - 10}{15}
   \]

3. Now, add the fractions:
   \[
   \frac{3x + 9}{15} + \frac{5x - 10}{15} = \frac{(3x + 9) + (5x - 10)}{15}
   \]
   Simplify the numerator:
   \[
   (3x + 9) + (5x - 10) = 3x + 5x + 9 - 10 = 8x - 1
   \]

4. The simplified expression is:
   \[
   \frac{8x - 1}{15}
   \]

Would you like further explanation or have any questions?

Here are 5 related questions to deepen understanding:

1. How do you find the least common denominator of multiple fractions?
2. Can you simplify a fraction by factoring the numerator and denominator?
3. What happens when you subtract fractions with different denominators?
4. How do you solve an equation that involves fractions like these?
5. What are some real-world problems where adding fractions is useful?

**Tip:** Always simplify fractions by finding the least common denominator before adding or subtracting them!

Learn how to simplify the algebraic expression (x+3)/5 + (x-2)/3 by finding the least common denominator (LCD). This step-by-step guide covers key concepts like fraction addition and simplifying expressions, ideal for Grades 7-9 students.

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