Math Problem Statement

Simplify the mathematical expression containing nested fractions and square roots as depicted in the image.

Solution

The provided image contains a mathematical expression that appears to involve nested fractions and variables. Here's the expression as I interpret it:

x2x3x21\frac{\frac{x_2}{x_3}}{\frac{\sqrt{x_2}}{1}}

Simplification Steps:

  1. Start by rewriting the expression: x2x3x21=x2/x3x2\frac{\frac{x_2}{x_3}}{\frac{\sqrt{x_2}}{1}} = \frac{x_2 / x_3}{\sqrt{x_2}}

  2. Multiply the numerator by the reciprocal of the denominator: x2x3÷x2=x2x3x2\frac{x_2}{x_3} \div \sqrt{x_2} = \frac{x_2}{x_3 \cdot \sqrt{x_2}}

  3. Combine terms under the square root: x2x3x2=x2x2x3x2=x2x3\frac{x_2}{x_3 \cdot \sqrt{x_2}} = \frac{\sqrt{x_2} \cdot \sqrt{x_2}}{x_3 \cdot \sqrt{x_2}} = \frac{\sqrt{x_2}}{x_3}

Final Answer:

x2x3\frac{\sqrt{x_2}}{x_3}


Would you like further clarification or a deeper breakdown of these steps?


Related Questions:

  1. How do you simplify complex fractions involving square roots?
  2. What are the rules for combining square roots in fractions?
  3. How do you rationalize a fraction with square roots?
  4. What is the physical interpretation of such an expression in physics or engineering?
  5. Can this result be extended for x2x_2 or x3x_3 in terms of inequalities?

Tip:

Always simplify fractions step by step and remember that dividing by a fraction is equivalent to multiplying by its reciprocal!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Fractions
Square Roots

Formulas

Reciprocal property of fractions: \( \frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b} \)
Square root simplification: \( \sqrt{x} \cdot \sqrt{x} = x \)

Theorems

Properties of fractions
Rules of exponents and radicals

Suitable Grade Level

Grades 9-11