Math Problem Statement

(x + 6)^3 (√x - 2)^2 + (√x - 2)^2 (5x - 1)^2 / x

Solution

The expression simplifies to:

(x−2)2((x+6)3+(5x−1)2+1)x\frac{(\sqrt{x} - 2)^2 \left( (x + 6)^3 + (5x - 1)^2 + 1 \right)}{x}

Would you like more details or have any further questions?

Here are 5 related questions:

  1. How do we handle square roots in algebraic expressions?
  2. What methods can simplify more complex algebraic fractions?
  3. How does the distribution of terms impact simplification?
  4. Can we factor expressions involving square roots?
  5. What are the conditions for an expression like 1x\frac{1}{x} to be undefined?

Tip: Always check the domain of expressions involving square roots and denominators to avoid undefined results.

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Math Problem Analysis

Mathematical Concepts

Algebraic Expressions
Simplification
Square Roots

Formulas

(a + b)^n
(√x - a)^2
(x^n / x = x^(n-1))

Theorems

Distributive Property
Power of a Power Rule

Suitable Grade Level

Grades 10-12

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