# The Types of Algebraic Expression

From the numbers and variables with the helping of sign of addition, subtraction, multiplication, division, raising to rational power and root extraction and with the helping of bracket we can compose the **algebraic expression**.

The examples of algebraic expression:

- `2a^2b-3ab^2*(a+b)` ;
- `a+b+(c/5)` ;
- `(3a^2+3a+1)/(a-1)` ;
- `(1/a+1/b-c/3)^3` ;
- `sqrt(a+b)` ;
- `(root(3)(2)-x)^4` ;
- `a^(3/2)-b^(3/2)` .

If the algebraic expression doesn′t contain the division by variables (i.a. exponentiation with a fractional exponent), then it is called **integral**.

The integral expressions from written above are expressions 1, 2 and 6.

If algebraic expression consists of numbers and variables with the helping of operations of addition, subtraction, multiplication, exponentiation with the natural exponent and division, and besides division by expression with variables, then it is called **fractional**.

The fractional expressions from written above are expressions 3 and 4.

The integral and fractional expressions are called **rational** expressions.

For example, the rational expressions from written above are expressions 1, 2, 3, 4 and 6.

If we use root extraction from variables (or raising to fractional power) in the algebraic expression, then such expression is called **irrational**.

The irrational expressions from written above are expressions 5 and 7.

So, algebraic expression can be rational and irrational. Rational expressions are divided into integral and fractional.