It looks like you're trying to simplify an expression. I'll assume you meant:

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

To simplify this, let's find a common denominator and proceed with the addition.

1. The least common denominator (LCD) for \(\frac{5x}{2x - y}\) and \(\frac{y}{3x - y}\) is \((2x - y)(3x - y)\).

2. Rewrite each fraction with the LCD:

   \[
   \frac{5x \cdot (3x - y)}{(2x - y)(3x - y)} + \frac{y \cdot (2x - y)}{(2x - y)(3x - y)}
   \]

3. Expand each term in the numerator:

   - For the first term: \(5x \cdot (3x - y) = 15x^2 - 5xy\)
   - For the second term: \(y \cdot (2x - y) = 2xy - y^2\)

   So, we have:

   \[
   \frac{15x^2 - 5xy + 2xy - y^2}{(2x - y)(3x - y)}
   \]

4. Combine like terms in the numerator:

   \[
   \frac{15x^2 - 3xy - y^2}{(2x - y)(3x - y)}
   \]

This expression, \(\frac{15x^2 - 3xy - y^2}{(2x - y)(3x - y)}\), is simplified as much as possible unless further factoring is possible in the numerator. 

Would you like more details or have any questions?

---

**Related questions:**

1. How do we find a common denominator for adding fractions with variables?
2. Can this expression be simplified further if we know specific values for \(x\) and \(y\)?
3. How does factoring help in simplifying algebraic expressions?
4. What happens if \(2x - y = 0\) or \(3x - y = 0\) in this expression?
5. Why is it important to simplify expressions in algebra?

**Tip:** Always double-check the common denominator before adding fractions to ensure accuracy.

Discover the step-by-step solution to simplify the expression 5x/(2x - y) + y/(3x - y) by finding a common denominator and combining terms. This problem covers essential algebraic techniques for handling rational expressions and is ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation