Math Problem Statement

Simplify the expression \(\frac{1}{\sqrt{x} - 2} - \frac{3}{x - 8}\).

Solution

The mathematical expression in the image is:

1x23x8\frac{1}{\sqrt{x} - 2} - \frac{3}{x - 8}

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Related Questions:

  1. Would you like the domain of this expression?
  2. Should I simplify this into a single fraction?
  3. Do you want me to check any potential restrictions for xx?
  4. Would you like to see a graph of this function?
  5. Should I solve for xx in a specific context (e.g., setting the expression equal to 0)?

Tip:

Always verify the domain of any rational or radical expression to ensure that the denominator or square roots are not undefined!

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Math Problem Analysis

Mathematical Concepts

Simplification of rational expressions
Radical expressions
Algebraic subtraction

Formulas

Common denominator rule for subtracting fractions
Simplification of terms involving radicals

Theorems

Basic properties of rational functions

Suitable Grade Level

Grades 10-12