https://file.aiquickdraw.com/mathbot/file/1733001519950abbaodst.jpg

 sympy import symbols, sqrt, simplify

# Define the variables and expression
x = symbols('x')
expression = (-(x**2 + 1)**(1/2) + x**2 * (x**2 + 1)**(-1/2)) / x**2

# Simplify the expression
simplified_expression = simplify(expression)
simplified_expressionThe simplified expression is:

\[
(x^2 + 1)^{-1/2} - \frac{(x^2 + 1)^{1/2}}{x^2}
\]

Would you like further details on the steps involved in the simplification or any other aspect of this problem?

Here are five related questions for exploration:
1. How does the exponentiation rule apply in simplifying this expression?
2. What are the conditions under which this expression is defined?
3. How can this expression be further analyzed for its limits as \(x \to 0\) or \(x \to \infty\)?
4. How would this expression look when differentiated with respect to \(x\)?
5. What are some real-world applications of such expressions in mathematical physics or engineering?

**Tip**: Always look for opportunities to factorize or find common terms when simplifying algebraic expressions.

Simplify the expression -((x^2 + 1)^(1/2) + x^2 * (x^2 + 1)^(-1/2)) / x^2.

Explore the detailed steps to simplify the algebraic expression -((x^2 + 1)^(1/2) + x^2 * (x^2 + 1)^(-1/2)) / x^2. This problem applies laws of exponents and fraction simplification, suitable for students in Grades 11-12.

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