Math Problem Statement

Simplify the expression \(\frac{x - 5}{\sqrt{x} - \sqrt{5}}\).

Solution

The expression in the image appears to be:

x5x5\frac{x - 5}{\sqrt{x} - \sqrt{5}}

Would you like to simplify this expression, or is there another operation you'd like to perform on it? Let me know if you'd like a detailed explanation or solution!

Here are 5 related questions that might expand this concept:

  1. How do you rationalize a denominator involving square roots?
  2. What is the limit of this expression as xx approaches 5?
  3. Can you factor any part of this expression further?
  4. How does this expression behave for large values of xx?
  5. How does this type of fraction relate to solving equations involving square roots?

Tip: When simplifying expressions with square roots, multiplying by the conjugate can help eliminate the square roots in the denominator.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rationalization
Square Roots

Formulas

Rationalization: Multiply by the conjugate
Square Root Properties

Theorems

Conjugate Method

Suitable Grade Level

Grades 10-12