https://r2.erweima.ai/mathbot/image/172616777538957nxlred.jpg

I see the math problems from the image you uploaded. Let's work through the ones I can see.

Here are the visible exercises:

1. \( \frac{2x^2 y^2}{3ab} \div \frac{9a^2b}{8xy} \)
2. \( \frac{3x + 3y}{x} - \frac{x^2}{6(x + y)} \)

### Problem 1:
\[
\frac{2x^2 y^2}{3ab} \div \frac{9a^2b}{8xy}
\]

To solve this, we first rewrite the division as multiplication by the reciprocal:
\[
\frac{2x^2 y^2}{3ab} \times \frac{8xy}{9a^2b}
\]

Now multiply the numerators and the denominators:
\[
\frac{2x^2 y^2 \cdot 8xy}{3ab \cdot 9a^2b} = \frac{16x^3 y^3}{27a^3 b^2}
\]

This is the simplified form.

### Problem 2:
\[
\frac{3x + 3y}{x} - \frac{x^2}{6(x + y)}
\]

First, simplify both terms individually.

For the first term:
\[
\frac{3x + 3y}{x} = 3 + \frac{3y}{x}
\]

For the second term:
\[
\frac{x^2}{6(x + y)}
\]

So the expression becomes:
\[
\left( 3 + \frac{3y}{x} \right) - \frac{x^2}{6(x + y)}
\]

This is the simplified form, though we could further manipulate it by finding a common denominator if needed.

---

Do you need further clarification on these steps, or help with the remaining problems?

Here are 5 related questions to extend your understanding:

1. How do you divide two algebraic fractions?
2. What are the general rules for simplifying rational expressions?
3. How would you handle a problem where the division involves negative exponents?
4. What is the importance of factoring when simplifying fractions?
5. How do you approach complex fractions with polynomials in both the numerator and denominator?

### Tip:
Always check if you can cancel out terms before performing multiplications or divisions in rational expressions.

Complete the exercises from the provided image.

This solution covers algebraic problems involving the division of rational expressions and simplification of algebraic fractions. Concepts like multiplying by reciprocals and simplifying terms are key. Suitable 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