Math Problem Statement
Simply the expression x^2/sqrt(1+x^2) so that only a 1 remains in the denominator
Solution
To simplify the expression such that only a 1 remains in the denominator, we can multiply both the numerator and denominator by . Here's how the simplification works:
Now, the denominator becomes , which simplifies the expression to:
This is the simplified expression with a denominator of .
Would you like more details or explanations on this step? Here are 5 related questions you might explore:
- How would the result change if the denominator was instead?
- What happens if we substitute specific values for in the simplified expression?
- How can we further manipulate this expression for ?
- What are the possible interpretations of this expression in calculus?
- Can you express the original function as a Taylor series around ?
Tip: Simplifying expressions often involves multiplying by clever forms of 1 (like ) to achieve the desired form.
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplification
Rationalization of Denominators
Radicals
Formulas
Rationalizing a denominator using sqrt(1 + x^2)
Theorems
Rationalization theorem for expressions with radicals
Suitable Grade Level
Grades 10-12