MHB State the differences between an expression and its simplified equivalent.

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The primary difference between an expression and its simplified equivalent lies in the presence of removable singularities, as illustrated by the example f(x) = x/x, which simplifies to f(x) = 1 for x ≠ 0. The simplified expression is generally considered simpler and more straightforward. However, understanding these differences often requires context from specific courses or textbooks that define terms like "expression," "simplified," and "equivalent." Such educational materials typically provide examples that clarify the process of simplification. Overall, context is essential for accurately discussing the differences between expressions and their simplified forms.
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State the differences between an expression and its simplified equivalent.
 
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The main difference that comes to my mind is that of removable singularities. For example, consider:

$$f(x)=\frac{x}{x}$$

This is the same as :

$$f(x)=1$$ where $$x\ne0$$
 
arroww said:
State the differences between an expression and its simplified equivalent.
The only think that I can say is that the second expression is presumably simpler. Unfortunately, it is not possible to answer this question outside the context of a particular course or book. This context must provide definitions for such concepts and "expression", "simplified" and "equivalent". I would guess the course or book also give a number of examples of simplifications that can help answer the question.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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