# Algebraic Expression

An Algebraic Expression is a mathematical expression that is composed of constants, free variables and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).

**Context:**- It can be referenced by an Algebraic Equation or an Algebraic Function or ...

**Example(s):**- [math]\displaystyle{ \sqrt{\frac{1-x^2}{1+x^2}} }[/math].

**See:**Square Root, Expression (Mathematics), Linguistic Expression.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/algebraic_expression Retrieved:2014-11-23.
- In mathematics, an
**algebraic expression**is an expression built up from constants, variables, and the algebraic operations (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number). For example, [math]\displaystyle{ 3x^2 - 2xy + c }[/math] is an algebraic expression. Since taking the square root is the same as raising to the power [math]\displaystyle{ \tfrac{1}{2} }[/math], :[math]\displaystyle{ \sqrt{\frac{1-x^2}{1+x^2}} }[/math]is also an algebraic expression.

A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other words, a rational expression is an expression which may be constructed from the variables and the constants by using only the four operations of arithmetic. Thus, [math]\displaystyle{ 3x^2 - 2xy + c }[/math] is a rational expression, whereas [math]\displaystyle{ \sqrt{\frac{1-x^2}{1+x^2}} }[/math] is not.

A

**rational equation**is an equation in which two rational fractions (or rational expressions) of the form [math]\displaystyle{ \frac{P(x)}{Q(x)} }[/math] are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.

- In mathematics, an

### 2011

- http://en.wikipedia.org/wiki/Algebraic_sentence
- In mathematical logic, an
**algebraic sentence**is one that can be stated using only equations between terms with free variables. Inequalities and quantifiers are specifically disallowed. Sentential logic is the subset of first-order logic involving only algebraic sentences.Saying that a sentence is algebraic is a stronger condition than saying it is elementary.

- In mathematical logic, an