Math Problem Statement

Multiplying and Dividing Rational Expressions (version 1): Solve the given rational expression problems.

Solution

The image you uploaded contains math problems on multiplying and dividing rational expressions. Let me extract the details and help you solve them. Please give me a moment.Here are the exercises based on multiplying and dividing rational expressions in the image:

  1. x24520x×3xx2\frac{x^2}{45 - 20x} \times \frac{3 - x}{x - 2}
  2. 37÷xx+1\frac{3}{7} \div \frac{x}{x + 1}
  3. 3x2x2×x+53x+15\frac{3x^2}{x - 2} \times \frac{x + 5}{3x + 15}
  4. 3x9x+3÷x3x+4\frac{3x - 9}{x + 3} \div \frac{x - 3}{x + 4}
  5. x29x4×1x7\frac{x^2 - 9x}{4} \times \frac{1}{x - 7}
  6. x2+xx+7×x2+7xx2\frac{x^2 + x}{x + 7} \times \frac{x^2 + 7x}{x^2}

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Expressions
Factoring
Simplification
Division of Fractions
Multiplication of Fractions

Formulas

Multiplication of rational expressions: (a/b) * (c/d) = (a * c) / (b * d)
Division of rational expressions: (a/b) ÷ (c/d) = (a/b) * (d/c)
Factoring quadratic expressions: ax^2 + bx + c
Simplifying expressions by canceling common factors

Theorems

Fundamental Theorem of Algebra
Properties of Fractions
Factoring Theorem

Suitable Grade Level

Grades 8-10