# Allowable Value of Variables. Domain of Algebraic Expression

The values of variables, for which the algebraic expression makes sense, are called **allowable values of variables**. The set of all allowable values of variables is called **domain of algebraic expression**.

The integral expression has sense for any values of variables, that it contains.

So, for all values of variables make sense of integral expressions such as ` 2a^2b-3ab^2*(a+b); a+b+(c/5); (root(3)(2)-x)^4 ` .

The fractional expressions don′t make sense for values of variables, that convert the denominator into zero.

For example, the fractional expression `(3a^2+3a+1)/(a-1)` has sense for all `a`, besides `a=1` and the fractional expression `(1/a+1/b-c/3)^3` - for all `a, b, c` , besides the values `a=0, b=0` .

The irrational expression doesn′t make sense for all values of variables, that make expression negative under root of even degree or under sign of raising to fractional degree.

For example, the irrational expression `sqrt(a+b)` makes sense only for those `a,b,` for which `a+b>=0` and irrational expression `a^(3/2)-b^(3/2)` - only for `a>=0` and `b>=0`.

If we attach the allowable value to the variables into algebraic expression we will obtain numerical expression; its value is called the **value of algebraic expression** for selected values of th variables.

For example, we have the value of expression `(root(3)(a^2+b))/(2a-b)` and for `a=5, b=2` we will find by the substituting these values of variables in this expression: `root(3)(5^2+2)/(2*5-2)=root(3)(27)/(10-2)=3/8` .