State the differences between an expression and its simplified equivalent.

In summary, the main difference between an expression and its simplified equivalent is that the latter typically involves removable singularities. This means that certain values of the variable may not be defined in the original expression, but are defined in the simplified form. Additionally, the simplified form is assumed to be simpler, but this can vary depending on the context and the definitions provided in a specific course or book. Examples and further explanations may be necessary to fully understand the differences between an expression and its simplified equivalent.
  • #1
arroww
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State the differences between an expression and its simplified equivalent.
 
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  • #2
The main difference that comes to my mind is that of removable singularities. For example, consider:

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

This is the same as :

\(\displaystyle f(x)=1\) where \(\displaystyle x\ne0\)
 
  • #3
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.
 

FAQ: State the differences between an expression and its simplified equivalent.

What is an expression?

An expression is a combination of numbers, variables, and mathematical operations that represents a value. It can also include functions, exponents, and other mathematical symbols.

What is a simplified equivalent?

A simplified equivalent is an expression that has been simplified or reduced to its simplest form using mathematical rules and properties. It has the same value as the original expression, but is written in a simpler and more organized way.

What are the differences between an expression and its simplified equivalent?

The main difference is that an expression can be more complex and may contain more terms and operations, while its simplified equivalent is simpler and contains fewer terms and operations. Additionally, an expression may include variables, while a simplified equivalent may not.

Why is it important to simplify an expression?

Simplifying an expression makes it easier to understand and work with. It also helps to identify patterns and relationships between different expressions. In some cases, simplifying an expression can also help to solve equations or find solutions to problems.

How do you simplify an expression?

To simplify an expression, you can use mathematical rules and properties such as the distributive property, combining like terms, and using the order of operations. You can also use algebraic techniques such as factoring and substitution to simplify more complex expressions.

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